← C3×D3×H(3,𝔽4) #11910203
Subgroups — C3×D3×H(3,𝔽4) #11910203
Order 1152.
2946 conjugacy classes of subgroups.
The subgroup lattice has 284 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C32×H(3,𝔽4) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#5683 | C2 | 1 | 9 | yes | maximal, complemented |
| 3 | C3×D3×#124 | C2 | 1 | 9 | yes | maximal, complemented |
| 4 | C3×#5594 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | C3×D3×#120 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | C2×C3×H(3,𝔽4) | — | 3 | 1 | no | maximal |
| 7 | D3×H(3,𝔽4) | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 8 | C24×C3×D3 | C22 | 1 | 2 | yes | complemented |
| 9 | C2×C3×D3×Q8 | C22 | 1 | 3 | yes | complemented |
| 10 | C2×C3×D3×D4 | C22 | 1 | 9 | yes | — |
| 11 | C32×#124 | C22 | 1 | 9 | yes | complemented |
| 12 | C32×#120 | C22 | 1 | 6 | yes | complemented |
| 13 | C3×#953 | C22 | 1 | 6 | yes | complemented |
| 14 | C3×#947 | C22 | 1 | 9 | yes | complemented |
| 15 | C3×#937 | C22 | 1 | 18 | yes | complemented |
| 16 | C3×#936 | C22 | 1 | 9 | yes | complemented |
| 17 | C3×#885 | C22 | 1 | 36 | yes | complemented |
| 18 | C3×#882 | C22 | 1 | 18 | yes | complemented |
| 19 | C3×D3×C22⋊C4 | C22 | 1 | 18 | yes | complemented |
| 20 | C3×#875 | C22 | 1 | 9 | yes | complemented |
| 21 | C3×C42×D3 | C22 | 1 | 3 | yes | complemented |
| 22 | C3×H(3,𝔽4) | — | 2 | 1 | no | — |
| 23 | C3×H(3,𝔽4) | — | 3 | 9 | no | — |
| 24 | C3×H(3,𝔽4) | — | 3 | 6 | no | — |
| 25 | C3×H(3,𝔽4) | D3 | 1 | 1 | yes | characteristic, direct product factor |
| 26 | C3×H(3,𝔽4) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×C3×#124 | — | 3 | 9 | no | — |
| 28 | C2×C3×#120 | — | 3 | 6 | no | — |
| 29 | #5683 | C2×C3 | 1 | 9 | yes | complemented |
| 30 | D3×#124 | C2×C3 | 1 | 9 | yes | complemented |
| 31 | #5594 | C2×C3 | 1 | 6 | yes | complemented |
| 32 | D3×#120 | C2×C3 | 1 | 6 | yes | complemented |
| 33 | C24×C32 | C23 | 1 | 2 | yes | complemented |
| 34 | C23×C3×D3 | — | 4 | 12 | no | — |
| 35 | C23×C3×D3 | C23 | 1 | 6 | yes | — |
| 36 | C23×C3×D3 | C23 | 1 | 6 | yes | complemented |
| 37 | C2×C32×Q8 | C23 | 1 | 3 | yes | complemented |
| 38 | C2×C32×D4 | C23 | 1 | 9 | yes | — |
| 39 | C2×C3×#67 | C23 | 1 | 18 | yes | — |
| 40 | C3×D3×Q8 | — | 4 | 6 | no | — |
| 41 | C3×D3×D4 | — | 4 | 18 | no | — |
| 42 | C2×C3×D12 | C23 | 1 | 9 | yes | — |
| 43 | C2×C3×C4×D3 | C23 | 1 | 9 | yes | — |
| 44 | C2×C3×Dic6 | C23 | 1 | 9 | yes | complemented |
| 45 | C32×C22⋊C4 | C23 | 1 | 18 | yes | complemented |
| 46 | C32×C42 | C23 | 1 | 3 | yes | complemented |
| 47 | C3×#217 | C23 | 1 | 18 | yes | complemented |
| 48 | C3×(C2×D3)⋊C4 | C23 | 1 | 36 | yes | complemented |
| 49 | C3×C4×Dic3 | C23 | 1 | 9 | yes | complemented |
| 50 | C2×H(3,𝔽4) | — | 3 | 1 | no | Sylow |
| 51 | C25×C3 | — | 3 | 2 | no | — |
| 52 | C24×D3 | C22×C3 | 1 | 2 | yes | complemented |
| 53 | C22×C3×Q8 | — | 3 | 3 | no | — |
| 54 | C22×C3×D4 | — | 3 | 9 | no | — |
| 55 | C2×D3×Q8 | C22×C3 | 1 | 3 | yes | complemented |
| 56 | C2×D3×D4 | C22×C3 | 1 | 9 | yes | — |
| 57 | C3×#124 | — | 2 | 9 | no | — |
| 58 | C3×#124 | — | 3 | 9 | no | — |
| 59 | C3×#124 | — | 3 | 9 | no | — |
| 60 | C3×#124 | — | 3 | 36 | no | — |
| 61 | C3×#124 | — | 3 | 9 | no | — |
| 62 | C3×#124 | C2×D3 | 1 | 9 | yes | complemented |
| 63 | C3×#124 | C22×C3 | 1 | 9 | yes | complemented |
| 64 | C3×#120 | — | 2 | 6 | no | — |
| 65 | C3×#120 | — | 3 | 6 | no | — |
| 66 | C3×#120 | — | 3 | 18 | no | — |
| 67 | C3×#120 | — | 3 | 18 | no | — |
| 68 | C3×#120 | C2×D3 | 1 | 6 | yes | complemented |
| 69 | C3×#120 | C22×C3 | 1 | 6 | yes | complemented |
| 70 | C2×C3×C22⋊C4 | — | 3 | 18 | no | — |
| 71 | C2×C3×C42 | — | 3 | 3 | no | — |
| 72 | #953 | C22×C3 | 1 | 6 | yes | complemented |
| 73 | #947 | C22×C3 | 1 | 9 | yes | complemented |
| 74 | #937 | C22×C3 | 1 | 18 | yes | complemented |
| 75 | #936 | C22×C3 | 1 | 9 | yes | complemented |
| 76 | #885 | C22×C3 | 1 | 36 | yes | complemented |
| 77 | #882 | C22×C3 | 1 | 18 | yes | complemented |
| 78 | D3×C22⋊C4 | C22×C3 | 1 | 18 | yes | complemented |
| 79 | #875 | C22×C3 | 1 | 9 | yes | complemented |
| 80 | C42×D3 | C22×C3 | 1 | 3 | yes | complemented |
| 81 | C23×C32 | — | 4 | 6 | no | — |
| 82 | C23×C32 | C24 | 1 | 6 | yes | — |
| 83 | C22×C3×D3 | — | 2 | 36 | no | — |
| 84 | C22×C3×D3 | — | 4 | 18 | no | — |
| 85 | C22×C3×D3 | — | 4 | 32 | no | — |
| 86 | C22×C3×D3 | C24 | 1 | 6 | yes | — |
| 87 | C22×C3×D3 | C24 | 1 | 1 | yes | characteristic |
| 88 | C32×Q8 | — | 4 | 3 | no | — |
| 89 | C32×D4 | — | 4 | 9 | no | — |
| 90 | C2×C32×C4 | C24 | 1 | 9 | yes | — |
| 91 | C3×#67 | — | 4 | 18 | no | — |
| 92 | C2×C3×Dic3 | C24 | 1 | 9 | yes | — |
| 93 | C3×D12 | — | 4 | 9 | no | — |
| 94 | C3×C4×D3 | — | 2 | 18 | no | — |
| 95 | C3×Dic6 | — | 4 | 9 | no | — |
| 96 | H(3,𝔽4) | — | 3 | 9 | no | — |
| 97 | H(3,𝔽4) | — | 3 | 6 | no | — |
| 98 | H(3,𝔽4) | C3×D3 | 1 | 1 | yes | characteristic, direct product factor |
| 99 | C2×#124 | — | 3 | 9 | no | — |
| 100 | C2×#120 | — | 3 | 6 | no | — |
| 101 | C24×C3 | — | 2 | 2 | no | — |
| 102 | C24×C3 | — | 3 | 6 | no | — |
| 103 | C24×C3 | — | 3 | 6 | no | — |
| 104 | C24×C3 | — | 12 | 12 | no | — |
| 105 | C24×C3 | C22×D3 | 1 | 2 | yes | complemented |
| 106 | C24×C3 | C23×C3 | 1 | 2 | yes | complemented |
| 107 | C23×D3 | — | 4 | 12 | no | — |
| 108 | C23×D3 | C23×C3 | 1 | 6 | yes | — |
| 109 | C23×D3 | C23×C3 | 1 | 6 | yes | complemented |
| 110 | C2×C3×Q8 | — | 2 | 3 | no | — |
| 111 | C2×C3×Q8 | — | 3 | 9 | no | — |
| 112 | C2×C3×Q8 | — | 12 | 6 | no | — |
| 113 | C2×C3×Q8 | C22×D3 | 1 | 3 | yes | complemented |
| 114 | C2×C3×Q8 | C23×C3 | 1 | 3 | yes | complemented |
| 115 | C2×C3×D4 | — | 2 | 9 | no | — |
| 116 | C2×C3×D4 | — | 3 | 18 | no | — |
| 117 | C2×C3×D4 | — | 3 | 9 | no | — |
| 118 | C2×C3×D4 | — | 12 | 18 | no | — |
| 119 | C2×C3×D4 | C22×D3 | 1 | 9 | yes | — |
| 120 | C2×C3×D4 | C23×C3 | 1 | 9 | yes | — |
| 121 | C22×C3×C4 | — | 3 | 9 | no | — |
| 122 | C2×#67 | C23×C3 | 1 | 18 | yes | — |
| 123 | D3×Q8 | — | 4 | 6 | no | — |
| 124 | D3×D4 | — | 4 | 18 | no | — |
| 125 | C2×D12 | C23×C3 | 1 | 9 | yes | — |
| 126 | C2×C4×D3 | C23×C3 | 1 | 9 | yes | — |
| 127 | C2×Dic6 | C23×C3 | 1 | 9 | yes | complemented |
| 128 | C3×C22⋊C4 | — | 2 | 18 | no | — |
| 129 | C3×C22⋊C4 | — | 3 | 18 | no | — |
| 130 | C3×C22⋊C4 | — | 3 | 36 | no | — |
| 131 | C3×C22⋊C4 | C22×D3 | 1 | 18 | yes | complemented |
| 132 | C3×C22⋊C4 | C23×C3 | 1 | 18 | yes | complemented |
| 133 | C3×C42 | — | 2 | 3 | no | — |
| 134 | C3×C42 | — | 3 | 9 | no | — |
| 135 | C3×C42 | C22×D3 | 1 | 3 | yes | complemented |
| 136 | C3×C42 | C23×C3 | 1 | 3 | yes | complemented |
| 137 | #217 | C23×C3 | 1 | 18 | yes | complemented |
| 138 | (C2×D3)⋊C4 | C23×C3 | 1 | 36 | yes | complemented |
| 139 | C4×Dic3 | C23×C3 | 1 | 9 | yes | complemented |
| 140 | C22×C32 | — | 2 | 18 | no | — |
| 141 | C22×C32 | — | 4 | 8 | no | — |
| 142 | C22×C32 | C25 | 1 | 1 | yes | characteristic |
| 143 | C2×C3×D3 | — | 2 | 18 | no | — |
| 144 | C2×C3×D3 | — | 4 | 24 | no | — |
| 145 | C2×C3×D3 | — | 4 | 24 | no | — |
| 146 | C2×C3×D3 | H(5,𝔽2) | 1 | 6 | yes | — |
| 147 | C32×C4 | — | 2 | 9 | no | — |
| 148 | C3×Dic3 | — | 2 | 9 | no | — |
| 149 | C25 | — | 3 | 2 | no | — |
| 150 | C22×Q8 | — | 3 | 3 | no | — |
| 151 | C22×D4 | — | 3 | 9 | no | — |
| 152 | #124 | — | 3 | 9 | no | — |
| 153 | #124 | — | 3 | 9 | no | — |
| 154 | #124 | — | 3 | 36 | no | — |
| 155 | #124 | — | 3 | 9 | no | — |
| 156 | #124 | C2×C3×D3 | 1 | 9 | yes | complemented |
| 157 | #120 | — | 3 | 6 | no | — |
| 158 | #120 | — | 3 | 18 | no | — |
| 159 | #120 | — | 3 | 18 | no | — |
| 160 | #120 | C2×C3×D3 | 1 | 6 | yes | complemented |
| 161 | C2×C22⋊C4 | — | 3 | 18 | no | — |
| 162 | C2×C42 | — | 3 | 3 | no | — |
| 163 | C23×C3 | — | 2 | 6 | no | — |
| 164 | C23×C3 | — | 3 | 1 | no | — |
| 165 | C23×C3 | — | 3 | 6 | no | — |
| 166 | C23×C3 | — | 4 | 6 | no | — |
| 167 | C23×C3 | — | 4 | 6 | no | — |
| 168 | C23×C3 | — | 6 | 36 | no | — |
| 169 | C23×C3 | — | 8 | 6 | no | — |
| 170 | C23×C3 | — | 12 | 18 | no | — |
| 171 | C23×C3 | — | 12 | 32 | no | — |
| 172 | C23×C3 | C23×D3 | 1 | 6 | yes | — |
| 173 | C23×C3 | C24×C3 | 1 | 6 | yes | — |
| 174 | C22×D3 | — | 2 | 36 | no | — |
| 175 | C22×D3 | — | 4 | 18 | no | — |
| 176 | C22×D3 | — | 4 | 32 | no | — |
| 177 | C22×D3 | C24×C3 | 1 | 6 | yes | — |
| 178 | C22×D3 | C24×C3 | 1 | 1 | yes | characteristic |
| 179 | C3×Q8 | — | 4 | 3 | no | — |
| 180 | C3×Q8 | — | 4 | 3 | no | — |
| 181 | C3×Q8 | — | 8 | 3 | no | — |
| 182 | C3×Q8 | — | 12 | 9 | no | — |
| 183 | C3×D4 | — | 4 | 9 | no | — |
| 184 | C3×D4 | — | 4 | 9 | no | — |
| 185 | C3×D4 | — | 8 | 9 | no | — |
| 186 | C3×D4 | — | 12 | 9 | no | — |
| 187 | C3×D4 | — | 12 | 18 | no | — |
| 188 | C2×C3×C4 | — | 2 | 9 | no | — |
| 189 | C2×C3×C4 | — | 3 | 9 | no | — |
| 190 | C2×C3×C4 | — | 6 | 18 | no | — |
| 191 | C2×C3×C4 | C23×D3 | 1 | 9 | yes | — |
| 192 | C2×C3×C4 | C24×C3 | 1 | 9 | yes | — |
| 193 | #67 | — | 4 | 18 | no | — |
| 194 | C2×Dic3 | C24×C3 | 1 | 9 | yes | — |
| 195 | D12 | — | 4 | 9 | no | — |
| 196 | C4×D3 | — | 2 | 18 | no | — |
| 197 | Dic6 | — | 4 | 9 | no | — |
| 198 | C2×C32 | — | 4 | 6 | no | — |
| 199 | C2×C32 | C2×H(5,𝔽2) | 1 | 3 | yes | — |
| 200 | C3×D3 | — | 4 | 6 | no | — |
| 201 | C3×D3 | H(3,𝔽4) | 1 | 4 | yes | direct product factor |
| 202 | C24 | — | 3 | 6 | no | — |
| 203 | C24 | — | 3 | 6 | no | — |
| 204 | C24 | — | 12 | 12 | no | — |
| 205 | C24 | C22×C3×D3 | 1 | 2 | yes | complemented |
| 206 | C2×Q8 | — | 3 | 9 | no | — |
| 207 | C2×Q8 | — | 12 | 6 | no | — |
| 208 | C2×Q8 | C22×C3×D3 | 1 | 3 | yes | complemented |
| 209 | C2×D4 | — | 3 | 18 | no | — |
| 210 | C2×D4 | — | 3 | 9 | no | — |
| 211 | C2×D4 | — | 12 | 18 | no | — |
| 212 | C2×D4 | C22×C3×D3 | 1 | 9 | yes | — |
| 213 | C22×C4 | — | 3 | 9 | no | — |
| 214 | C22⋊C4 | — | 3 | 18 | no | — |
| 215 | C22⋊C4 | — | 3 | 36 | no | — |
| 216 | C22⋊C4 | C22×C3×D3 | 1 | 18 | yes | complemented |
| 217 | C42 | — | 3 | 9 | no | — |
| 218 | C42 | C22×C3×D3 | 1 | 3 | yes | complemented |
| 219 | C22×C3 | — | 2 | 18 | no | — |
| 220 | C22×C3 | — | 2 | 18 | no | — |
| 221 | C22×C3 | — | 2 | 1 | no | — |
| 222 | C22×C3 | — | 3 | 6 | no | — |
| 223 | C22×C3 | — | 4 | 18 | no | — |
| 224 | C22×C3 | — | 4 | 8 | no | — |
| 225 | C22×C3 | — | 4 | 8 | no | — |
| 226 | C22×C3 | — | 6 | 18 | no | — |
| 227 | C22×C3 | — | 8 | 8 | no | — |
| 228 | C22×C3 | — | 12 | 24 | no | — |
| 229 | C22×C3 | — | 12 | 24 | no | — |
| 230 | C22×C3 | C24×D3 | 1 | 1 | yes | characteristic |
| 231 | C22×C3 | C25×C3 | 1 | 1 | yes | characteristic |
| 232 | C2×D3 | — | 2 | 18 | no | — |
| 233 | C2×D3 | — | 4 | 24 | no | — |
| 234 | C2×D3 | — | 4 | 24 | no | — |
| 235 | C2×D3 | C3×H(5,𝔽2) | 1 | 6 | yes | — |
| 236 | C3×C4 | — | 2 | 9 | no | — |
| 237 | C3×C4 | — | 2 | 9 | no | — |
| 238 | C3×C4 | — | 4 | 9 | no | — |
| 239 | C3×C4 | — | 6 | 9 | no | — |
| 240 | Dic3 | — | 2 | 9 | no | — |
| 241 | C32 | C2×H(3,𝔽4) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 242 | C23 | — | 3 | 1 | no | — |
| 243 | C23 | — | 3 | 6 | no | — |
| 244 | C23 | — | 4 | 6 | no | — |
| 245 | C23 | — | 6 | 36 | no | — |
| 246 | C23 | — | 12 | 18 | no | — |
| 247 | C23 | — | 12 | 32 | no | — |
| 248 | C23 | C23×C3×D3 | 1 | 6 | yes | — |
| 249 | Q8 | — | 4 | 3 | no | — |
| 250 | Q8 | — | 12 | 9 | no | — |
| 251 | D4 | — | 4 | 9 | no | — |
| 252 | D4 | — | 12 | 9 | no | — |
| 253 | D4 | — | 12 | 18 | no | — |
| 254 | C2×C4 | — | 3 | 9 | no | — |
| 255 | C2×C4 | — | 6 | 18 | no | — |
| 256 | C2×C4 | C23×C3×D3 | 1 | 9 | yes | — |
| 257 | C2×C3 | — | 2 | 3 | no | — |
| 258 | C2×C3 | — | 3 | 4 | no | — |
| 259 | C2×C3 | — | 4 | 6 | no | — |
| 260 | C2×C3 | — | 4 | 6 | no | — |
| 261 | C2×C3 | — | 8 | 6 | no | — |
| 262 | C2×C3 | — | 12 | 6 | no | — |
| 263 | C2×C3 | D3×H(5,𝔽2) | 1 | 3 | yes | — |
| 264 | C2×C3 | C2×C3×H(5,𝔽2) | 1 | 3 | yes | — |
| 265 | D3 | — | 4 | 6 | no | — |
| 266 | D3 | C3×H(3,𝔽4) | 1 | 4 | yes | direct product factor |
| 267 | C22 | — | 2 | 18 | no | — |
| 268 | C22 | — | 3 | 6 | no | — |
| 269 | C22 | — | 4 | 8 | no | — |
| 270 | C22 | — | 6 | 18 | no | — |
| 271 | C22 | — | 12 | 24 | no | — |
| 272 | C22 | — | 12 | 24 | no | — |
| 273 | C22 | C24×C3×D3 | 1 | 1 | yes | characteristic |
| 274 | C4 | — | 2 | 9 | no | — |
| 275 | C4 | — | 6 | 9 | no | — |
| 276 | C3 | — | 2 | 1 | no | — |
| 277 | C3 | D3×H(3,𝔽4) | 1 | 1 | yes | characteristic, direct product factor |
| 278 | C3 | C2×C3×H(3,𝔽4) | 1 | 1 | yes | characteristic, complemented |
| 279 | C2 | — | 3 | 4 | no | — |
| 280 | C2 | — | 4 | 6 | no | — |
| 281 | C2 | — | 12 | 6 | no | — |
| 282 | C2 | C3×D3×H(5,𝔽2) | 1 | 3 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 1. C32×H(3,𝔽4) | C2 | semidirect |
| 2. C3×#5683 | C2 | semidirect |
| 3. C3×D3×#124 | C2 | semidirect |
| 4. C3×#5594 | C2 | semidirect |
| 5. C3×D3×#120 | C2 | semidirect |
| 7. D3×H(3,𝔽4) | C3 | direct (N × H) |
| 8. C24×C3×D3 | C22 | semidirect |
| 9. C2×C3×D3×Q8 | C22 | semidirect |
| 11. C32×#124 | C22 | semidirect |
| 12. C32×#120 | C22 | semidirect |
| 13. C3×#953 | C22 | semidirect |
| 14. C3×#947 | C22 | semidirect |
| 15. C3×#937 | C22 | semidirect |
| 16. C3×#936 | C22 | semidirect |
| 17. C3×#885 | C22 | semidirect |
| 18. C3×#882 | C22 | semidirect |
| 19. C3×D3×C22⋊C4 | C22 | semidirect |
| 20. C3×#875 | C22 | semidirect |
| 21. C3×C42×D3 | C22 | semidirect |
| 25. C3×H(3,𝔽4) | D3 | direct (N × H) |
| 26. C3×H(3,𝔽4) | C2×C3 | semidirect |
| 29. #5683 | C2×C3 | semidirect |
| 30. D3×#124 | C2×C3 | semidirect |
| 31. #5594 | C2×C3 | semidirect |
| 32. D3×#120 | C2×C3 | semidirect |
| 33. C24×C32 | C23 | semidirect |
| 36. C23×C3×D3 | C23 | semidirect |
| 37. C2×C32×Q8 | C23 | semidirect |
| 44. C2×C3×Dic6 | C23 | semidirect |
| 45. C32×C22⋊C4 | C23 | semidirect |
| 46. C32×C42 | C23 | semidirect |
| 47. C3×#217 | C23 | semidirect |
| 48. C3×(C2×D3)⋊C4 | C23 | semidirect |
| 49. C3×C4×Dic3 | C23 | semidirect |
| 52. C24×D3 | C22×C3 | semidirect |
| 55. C2×D3×Q8 | C22×C3 | semidirect |
| 62. C3×#124 | C2×D3 | semidirect |
| 63. C3×#124 | C22×C3 | semidirect |
| 68. C3×#120 | C2×D3 | semidirect |
| 69. C3×#120 | C22×C3 | semidirect |
| 72. #953 | C22×C3 | semidirect |
| 73. #947 | C22×C3 | semidirect |
| 74. #937 | C22×C3 | semidirect |
| 75. #936 | C22×C3 | semidirect |
| 76. #885 | C22×C3 | semidirect |
| 77. #882 | C22×C3 | semidirect |
| 78. D3×C22⋊C4 | C22×C3 | semidirect |
| 79. #875 | C22×C3 | semidirect |
| 80. C42×D3 | C22×C3 | semidirect |
| 98. H(3,𝔽4) | C3×D3 | direct (N × H) |
| 105. C24×C3 | C22×D3 | semidirect |
| 106. C24×C3 | C23×C3 | semidirect |
| 109. C23×D3 | C23×C3 | semidirect |
| 113. C2×C3×Q8 | C22×D3 | semidirect |
| 114. C2×C3×Q8 | C23×C3 | semidirect |
| 127. C2×Dic6 | C23×C3 | semidirect |
| 131. C3×C22⋊C4 | C22×D3 | semidirect |
| 132. C3×C22⋊C4 | C23×C3 | semidirect |
| 135. C3×C42 | C22×D3 | semidirect |
| 136. C3×C42 | C23×C3 | semidirect |
| 137. #217 | C23×C3 | semidirect |
| 138. (C2×D3)⋊C4 | C23×C3 | semidirect |
| 139. C4×Dic3 | C23×C3 | semidirect |
| 156. #124 | C2×C3×D3 | semidirect |
| 160. #120 | C2×C3×D3 | semidirect |
| 201. C3×D3 | H(3,𝔽4) | direct (N × H) |
| 205. C24 | C22×C3×D3 | semidirect |
| 208. C2×Q8 | C22×C3×D3 | semidirect |
| 216. C22⋊C4 | C22×C3×D3 | semidirect |
| 218. C42 | C22×C3×D3 | semidirect |
| 241. C32 | C2×H(3,𝔽4) | semidirect |
| 266. D3 | C3×H(3,𝔽4) | direct (N × H) |
| 277. C3 | D3×H(3,𝔽4) | direct (N × H) |
| 278. C3 | C2×C3×H(3,𝔽4) | semidirect |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta