← Dic3×#4133 #14411515
Subgroups — Dic3×#4133 #14411515
Order 1920.
1144 conjugacy classes of subgroups.
The subgroup lattice has 324 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#91992 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C3×#4133 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | Dic3×#713 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11751782 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | Dic3×#700 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #11751767 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | Dic3×D5⋊C8 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C4×#4133 | — | 3 | 1 | no | maximal, Hall |
| 9 | C2×C3×#713 | C22 | 1 | 1 | yes | characteristic |
| 10 | #91992 | C4 | 1 | 8 | yes | complemented |
| 11 | C2×#6758 | C22 | 1 | 3 | yes | — |
| 12 | C2×D5⋊(C3⋊C8) | C22 | 1 | 3 | yes | — |
| 13 | C3×#4133 | C4 | 1 | 8 | yes | complemented |
| 14 | C2×C3×#700 | C22 | 1 | 3 | yes | — |
| 15 | C2×C3×D5⋊C8 | C22 | 1 | 3 | yes | — |
| 16 | Q8×Dic15 | C4 | 1 | 1 | yes | characteristic |
| 17 | C5×Q8×Dic3 | C4 | 1 | 1 | yes | characteristic |
| 18 | #91434 | C4 | 1 | 3 | yes | — |
| 19 | Dic3×D20 | C4 | 1 | 3 | yes | — |
| 20 | C4×D5×Dic3 | C22 | 1 | 3 | yes | — |
| 21 | #91358 | C22 | 1 | 3 | yes | — |
| 22 | #91169 | C22 | 1 | 6 | yes | — |
| 23 | Dic3×#170 | C22 | 1 | 1 | yes | characteristic |
| 24 | Dic3×#170 | C22 | 1 | 3 | yes | — |
| 25 | Dic3×#170 | C22 | 1 | 3 | yes | — |
| 26 | Dic3×#170 | C22 | 1 | 3 | yes | — |
| 27 | Dic3×#131 | — | 5 | 1 | no | maximal, Hall |
| 28 | C2×#4133 | — | 3 | 1 | no | — |
| 29 | C2×#4133 | D3 | 1 | 1 | yes | characteristic |
| 30 | C4×#713 | — | 3 | 1 | no | — |
| 31 | #65701 | — | 3 | 3 | no | — |
| 32 | #65701 | — | 3 | 3 | no | — |
| 33 | C4×#700 | — | 3 | 3 | no | — |
| 34 | C4×D5⋊C8 | — | 3 | 3 | no | — |
| 35 | C2×C3×C5×Q8 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | C3×#713 | C2×C4 | 1 | 4 | yes | — |
| 37 | C3×#713 | C2×C4 | 1 | 4 | yes | — |
| 38 | C2×C3×D20 | C2×C4 | 1 | 3 | yes | — |
| 39 | C2×C3×C4×D5 | C23 | 1 | 3 | yes | — |
| 40 | C2×D5×Dic3 | C2×C4 | 1 | 3 | yes | — |
| 41 | C2×D5×Dic3 | C2×C4 | 1 | 3 | yes | — |
| 42 | C2×C3⋊#170 | C23 | 1 | 1 | yes | characteristic |
| 43 | C2×C3⋊#170 | C23 | 1 | 3 | yes | — |
| 44 | #6758 | C2×C4 | 1 | 12 | yes | complemented |
| 45 | D5⋊(C3⋊C8) | C2×C4 | 1 | 12 | yes | complemented |
| 46 | C2×C3×#170 | C23 | 1 | 1 | yes | characteristic |
| 47 | C2×C3×#170 | C23 | 1 | 3 | yes | — |
| 48 | C3×#700 | C2×C4 | 1 | 12 | yes | complemented |
| 49 | C3×D5⋊C8 | C2×C4 | 1 | 12 | yes | complemented |
| 50 | C4⋊Dic15 | C2×C4 | 1 | 3 | yes | — |
| 51 | C4×Dic15 | C2×C4 | 1 | 3 | yes | — |
| 52 | C5×C4⋊Dic3 | C2×C4 | 1 | 3 | yes | — |
| 53 | C4×C5×Dic3 | C2×C4 | 1 | 3 | yes | — |
| 54 | #6665 | C2×C4 | 1 | 6 | yes | — |
| 55 | Dic3×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 56 | Dic3×Dic5 | C23 | 1 | 3 | yes | — |
| 57 | C2×C3×#131 | — | 5 | 1 | no | — |
| 58 | Dic3×#41 | — | 5 | 1 | no | — |
| 59 | C2×#948 | — | 5 | 1 | no | — |
| 60 | #5122 | — | 5 | 3 | no | — |
| 61 | Dic3×M16 | — | 5 | 3 | no | — |
| 62 | #5101 | — | 5 | 3 | no | — |
| 63 | C2×C8×Dic3 | — | 5 | 3 | no | — |
| 64 | C2×#713 | C2×D3 | 1 | 1 | yes | characteristic |
| 65 | #4133 | — | 3 | 8 | no | — |
| 66 | #4133 | Dic3 | 1 | 8 | yes | direct product factor |
| 67 | C2×#700 | — | 3 | 3 | no | — |
| 68 | C2×#700 | C2×D3 | 1 | 3 | yes | — |
| 69 | C2×D5⋊C8 | — | 3 | 3 | no | — |
| 70 | C2×D5⋊C8 | C2×D3 | 1 | 3 | yes | — |
| 71 | C4×C5×Q8 | — | 3 | 1 | no | — |
| 72 | Q8×Dic5 | — | 3 | 1 | no | — |
| 73 | #4039 | — | 3 | 3 | no | — |
| 74 | #4038 | — | 3 | 3 | no | — |
| 75 | C4×D20 | — | 3 | 3 | no | — |
| 76 | C42×D5 | — | 3 | 3 | no | — |
| 77 | #4002 | — | 3 | 6 | no | — |
| 78 | C4×#170 | — | 3 | 1 | no | — |
| 79 | C4×#170 | — | 3 | 3 | no | — |
| 80 | C4×#170 | — | 3 | 3 | no | — |
| 81 | C4×#170 | — | 3 | 3 | no | — |
| 82 | C4×#131 | — | 15 | 1 | no | Sylow |
| 83 | C22×C3×D5 | C22×C4 | 1 | 3 | yes | — |
| 84 | C3×C5×Q8 | C42 | 1 | 4 | yes | — |
| 85 | C2×C3×C4×C5 | C22×C4 | 1 | 3 | yes | — |
| 86 | C2×Dic15 | C22×C4 | 1 | 3 | yes | — |
| 87 | C2×Dic15 | C22×C4 | 1 | 1 | yes | characteristic |
| 88 | C2×C5×Dic3 | C22×C4 | 1 | 3 | yes | — |
| 89 | C2×C5×Dic3 | C22×C4 | 1 | 1 | yes | characteristic |
| 90 | C2×C3×Dic5 | C24 | 1 | 1 | yes | characteristic |
| 91 | C3×D20 | C42 | 1 | 12 | yes | — |
| 92 | C3×C4×D5 | C22×C4 | 1 | 6 | yes | — |
| 93 | C3×C4×D5 | C22×C4 | 1 | 6 | yes | — |
| 94 | D5×Dic3 | — | 2 | 6 | no | — |
| 95 | D5×Dic3 | — | 2 | 6 | no | — |
| 96 | C3⋊#170 | C22×C4 | 1 | 2 | yes | — |
| 97 | C3⋊#170 | C22×C4 | 1 | 6 | yes | — |
| 98 | C3×#170 | C22×C4 | 1 | 2 | yes | — |
| 99 | C3×#170 | C22×C4 | 1 | 6 | yes | — |
| 100 | C2×C3×#41 | — | 5 | 1 | no | — |
| 101 | C3×#131 | — | 5 | 8 | no | — |
| 102 | C2×C3×M16 | — | 5 | 3 | no | — |
| 103 | C22×C3×C8 | — | 5 | 3 | no | — |
| 104 | #948 | — | 5 | 8 | no | — |
| 105 | Q8×Dic3 | — | 5 | 1 | no | — |
| 106 | Q8×Dic3 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 107 | D4×Dic3 | — | 5 | 3 | no | — |
| 108 | D4×Dic3 | — | 5 | 3 | no | — |
| 109 | #926 | — | 5 | 3 | no | — |
| 110 | C2×C4×Dic3 | — | 5 | 3 | no | — |
| 111 | C2×#208 | — | 5 | 3 | no | — |
| 112 | C22×C3⋊C8 | — | 5 | 3 | no | — |
| 113 | #815 | — | 5 | 6 | no | — |
| 114 | C8×Dic3 | — | 5 | 3 | no | — |
| 115 | C8×Dic3 | — | 5 | 1 | no | — |
| 116 | C8×Dic3 | — | 5 | 3 | no | — |
| 117 | C8×Dic3 | — | 5 | 3 | no | — |
| 118 | C2×C5×Q8 | C4×D3 | 1 | 1 | yes | characteristic |
| 119 | #713 | C4×D3 | 1 | 4 | yes | — |
| 120 | #713 | C2×Dic3 | 1 | 4 | yes | — |
| 121 | C2×D20 | C4×D3 | 1 | 3 | yes | — |
| 122 | C2×C4×D5 | — | 3 | 3 | no | — |
| 123 | C2×C4×D5 | — | 3 | 3 | no | — |
| 124 | C2×C4×D5 | C22×D3 | 1 | 3 | yes | — |
| 125 | C2×#170 | — | 3 | 1 | no | — |
| 126 | C2×#170 | — | 3 | 3 | no | — |
| 127 | C2×#170 | C22×D3 | 1 | 1 | yes | characteristic |
| 128 | C2×#170 | C22×D3 | 1 | 3 | yes | — |
| 129 | #700 | — | 3 | 12 | no | — |
| 130 | #700 | C2×Dic3 | 1 | 12 | yes | complemented |
| 131 | D5⋊C8 | — | 3 | 12 | no | — |
| 132 | D5⋊C8 | C2×Dic3 | 1 | 12 | yes | complemented |
| 133 | C5×C4⋊C4 | — | 3 | 3 | no | — |
| 134 | C42×C5 | — | 3 | 3 | no | — |
| 135 | #685 | — | 3 | 6 | no | — |
| 136 | C4⋊Dic5 | — | 3 | 3 | no | — |
| 137 | C4×Dic5 | — | 3 | 3 | no | — |
| 138 | C4×Dic5 | — | 3 | 1 | no | — |
| 139 | C4×Dic5 | — | 3 | 3 | no | — |
| 140 | C2×#131 | — | 5 | 1 | no | — |
| 141 | C2×#131 | — | 15 | 1 | no | — |
| 142 | C4×#41 | — | 15 | 1 | no | — |
| 143 | #405 | — | 15 | 3 | no | — |
| 144 | #405 | — | 15 | 3 | no | — |
| 145 | C4×M16 | — | 15 | 3 | no | — |
| 146 | C2×C4×C8 | — | 15 | 3 | no | — |
| 147 | C22×C3×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 148 | C2×C3×D5 | — | 2 | 3 | no | — |
| 149 | C2×C3×D5 | — | 2 | 3 | no | — |
| 150 | C2×C3×D5 | C2×C42 | 1 | 6 | yes | — |
| 151 | C3×C4×C5 | C2×C42 | 1 | 6 | yes | — |
| 152 | Dic15 | — | 2 | 3 | no | — |
| 153 | Dic15 | #131 | 1 | 2 | yes | complemented |
| 154 | C3×Dic5 | C23×C4 | 1 | 1 | yes | characteristic |
| 155 | C3×Dic5 | C23×C4 | 1 | 1 | yes | characteristic |
| 156 | C5×Dic3 | — | 2 | 3 | no | — |
| 157 | C5×Dic3 | #131 | 1 | 2 | yes | complemented |
| 158 | C3×#41 | — | 5 | 4 | no | — |
| 159 | C3×#41 | — | 5 | 4 | no | — |
| 160 | C2×C3×Q8 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 161 | C2×C3×D4 | — | 5 | 3 | no | — |
| 162 | C22×C3×C4 | — | 5 | 3 | no | — |
| 163 | C22×Dic3 | — | 5 | 3 | no | — |
| 164 | C22×Dic3 | — | 5 | 3 | no | — |
| 165 | C3×M16 | — | 5 | 12 | no | — |
| 166 | C2×C3×C8 | — | 5 | 1 | no | — |
| 167 | C2×C3×C8 | — | 5 | 3 | no | — |
| 168 | C2×C3×C8 | — | 5 | 12 | no | — |
| 169 | #217 | — | 5 | 6 | no | — |
| 170 | C4⋊Dic3 | — | 5 | 3 | no | — |
| 171 | C4⋊Dic3 | C2×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 172 | C4×Dic3 | — | 5 | 3 | no | — |
| 173 | C4×Dic3 | — | 5 | 1 | no | — |
| 174 | C4×Dic3 | — | 5 | 3 | no | — |
| 175 | C4×Dic3 | C2×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 176 | #208 | — | 5 | 12 | no | — |
| 177 | C2×C3⋊C8 | — | 5 | 1 | no | — |
| 178 | C2×C3⋊C8 | — | 5 | 3 | no | — |
| 179 | C2×C3⋊C8 | — | 5 | 12 | no | — |
| 180 | C22×D5 | C2×C4×D3 | 1 | 3 | yes | — |
| 181 | C5×Q8 | C4×Dic3 | 1 | 4 | yes | — |
| 182 | C2×C4×C5 | — | 3 | 1 | no | — |
| 183 | C2×C4×C5 | — | 3 | 3 | no | — |
| 184 | C2×C4×C5 | C2×C4×D3 | 1 | 3 | yes | — |
| 185 | C2×Dic5 | — | 3 | 1 | no | — |
| 186 | C2×Dic5 | — | 3 | 3 | no | — |
| 187 | C2×Dic5 | C23×D3 | 1 | 1 | yes | characteristic |
| 188 | D20 | C4×Dic3 | 1 | 12 | yes | — |
| 189 | C4×D5 | — | 6 | 6 | no | — |
| 190 | C4×D5 | — | 6 | 6 | no | — |
| 191 | C4×D5 | C2×C4×D3 | 1 | 6 | yes | — |
| 192 | C4×D5 | C22×Dic3 | 1 | 6 | yes | — |
| 193 | #170 | — | 3 | 2 | no | — |
| 194 | #170 | — | 3 | 6 | no | — |
| 195 | #170 | C22×Dic3 | 1 | 2 | yes | — |
| 196 | #170 | C22×Dic3 | 1 | 6 | yes | — |
| 197 | C2×#41 | — | 5 | 1 | no | — |
| 198 | #131 | — | 5 | 8 | no | — |
| 199 | #131 | — | 15 | 8 | no | — |
| 200 | C2×M16 | — | 5 | 3 | no | — |
| 201 | C2×M16 | — | 15 | 3 | no | — |
| 202 | C22×C8 | — | 5 | 3 | no | — |
| 203 | C22×C8 | — | 15 | 3 | no | — |
| 204 | C4×Q8 | — | 3 | 1 | no | — |
| 205 | C4×Q8 | — | 15 | 1 | no | — |
| 206 | C4×D4 | — | 15 | 3 | no | — |
| 207 | C4×D4 | — | 15 | 3 | no | — |
| 208 | #117 | — | 15 | 3 | no | — |
| 209 | C2×C42 | — | 15 | 3 | no | — |
| 210 | #97 | — | 15 | 6 | no | — |
| 211 | C4×C8 | — | 15 | 1 | no | — |
| 212 | C4×C8 | — | 15 | 3 | no | — |
| 213 | C4×C8 | — | 15 | 3 | no | — |
| 214 | C4×C8 | — | 15 | 3 | no | — |
| 215 | C2×C3×C5 | C22×C42 | 1 | 1 | yes | characteristic |
| 216 | C2×C3×C5 | C2×#131 | 1 | 1 | yes | characteristic |
| 217 | C2×C3×C5 | C2×#131 | 1 | 1 | yes | characteristic |
| 218 | C3×D5 | — | 2 | 6 | no | — |
| 219 | C23×C3 | — | 5 | 3 | no | — |
| 220 | C3×Q8 | C4×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 221 | C3×D4 | — | 5 | 12 | no | — |
| 222 | C2×C3×C4 | — | 5 | 1 | no | — |
| 223 | C2×C3×C4 | — | 5 | 6 | no | — |
| 224 | C2×C3×C4 | — | 5 | 6 | no | — |
| 225 | C2×C3×C4 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 226 | C2×Dic3 | — | 5 | 1 | no | — |
| 227 | C2×Dic3 | — | 5 | 3 | no | — |
| 228 | C2×Dic3 | — | 10 | 6 | no | — |
| 229 | C2×Dic3 | — | 10 | 6 | no | — |
| 230 | C2×Dic3 | C22×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 231 | C2×Dic3 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 232 | C3×C8 | — | 5 | 2 | no | — |
| 233 | C3×C8 | — | 5 | 6 | no | — |
| 234 | C3⋊C8 | — | 5 | 2 | no | — |
| 235 | C3⋊C8 | — | 5 | 6 | no | — |
| 236 | C22×C5 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 237 | C2×D5 | — | 2 | 3 | no | — |
| 238 | C2×D5 | — | 2 | 3 | no | — |
| 239 | C2×D5 | C2×C4×Dic3 | 1 | 6 | yes | — |
| 240 | C4×C5 | — | 3 | 2 | no | — |
| 241 | C4×C5 | — | 6 | 3 | no | — |
| 242 | C4×C5 | C2×C4×Dic3 | 1 | 6 | yes | — |
| 243 | Dic5 | — | 3 | 2 | no | — |
| 244 | Dic5 | — | 6 | 3 | no | — |
| 245 | Dic5 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 246 | Dic5 | C23×Dic3 | 1 | 1 | yes | characteristic |
| 247 | #41 | — | 5 | 4 | no | — |
| 248 | #41 | — | 5 | 4 | no | — |
| 249 | C2×Q8 | D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 250 | C2×D4 | — | 5 | 3 | no | — |
| 251 | C22×C4 | — | 5 | 3 | no | — |
| 252 | C22×C4 | — | 15 | 3 | no | — |
| 253 | C22×C4 | — | 15 | 3 | no | — |
| 254 | M16 | — | 5 | 12 | no | — |
| 255 | M16 | — | 15 | 12 | no | — |
| 256 | C2×C8 | — | 5 | 1 | no | — |
| 257 | C2×C8 | — | 5 | 3 | no | — |
| 258 | C2×C8 | — | 5 | 12 | no | — |
| 259 | C2×C8 | — | 15 | 1 | no | — |
| 260 | C2×C8 | — | 15 | 3 | no | — |
| 261 | C2×C8 | — | 15 | 12 | no | — |
| 262 | C4⋊C4 | — | 3 | 3 | no | — |
| 263 | C4⋊C4 | — | 15 | 3 | no | — |
| 264 | C22⋊C4 | — | 15 | 6 | no | — |
| 265 | C42 | — | 3 | 3 | no | — |
| 266 | C42 | — | 15 | 1 | no | — |
| 267 | C42 | — | 15 | 3 | no | — |
| 268 | C42 | — | 15 | 3 | no | — |
| 269 | C3×C5 | C4×#131 | 1 | 1 | yes | characteristic, complemented, Hall |
| 270 | C22×C3 | — | 5 | 6 | no | — |
| 271 | C22×C3 | — | 10 | 3 | no | — |
| 272 | C22×C3 | — | 10 | 3 | no | — |
| 273 | C22×C3 | C23×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 274 | C3×C4 | — | 5 | 1 | no | — |
| 275 | C3×C4 | — | 5 | 1 | no | — |
| 276 | C3×C4 | C2×C4×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 277 | Dic3 | — | 2 | 3 | no | — |
| 278 | Dic3 | — | 5 | 2 | no | — |
| 279 | Dic3 | — | 10 | 3 | no | — |
| 280 | Dic3 | #4133 | 1 | 2 | yes | direct product factor |
| 281 | C2×C5 | D3×#131 | 1 | 1 | yes | characteristic |
| 282 | C2×C5 | D3×#131 | 1 | 1 | yes | characteristic |
| 283 | C2×C5 | C22×C4×Dic3 | 1 | 1 | yes | characteristic |
| 284 | D5 | — | 2 | 6 | no | — |
| 285 | C23 | — | 5 | 3 | no | — |
| 286 | Q8 | Dic3×AGL(1,𝔽5) | 1 | 4 | yes | — |
| 287 | D4 | — | 5 | 12 | no | — |
| 288 | C2×C4 | — | 3 | 1 | no | — |
| 289 | C2×C4 | — | 3 | 3 | no | — |
| 290 | C2×C4 | — | 5 | 1 | no | — |
| 291 | C2×C4 | — | 5 | 6 | no | — |
| 292 | C2×C4 | — | 5 | 6 | no | — |
| 293 | C2×C4 | — | 15 | 1 | no | — |
| 294 | C2×C4 | — | 15 | 3 | no | — |
| 295 | C2×C4 | — | 30 | 6 | no | — |
| 296 | C2×C4 | — | 30 | 6 | no | — |
| 297 | C2×C4 | C2×D3×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 298 | C8 | — | 5 | 2 | no | — |
| 299 | C8 | — | 5 | 6 | no | — |
| 300 | C8 | — | 15 | 2 | no | — |
| 301 | C8 | — | 15 | 6 | no | — |
| 302 | C2×C3 | — | 10 | 6 | no | — |
| 303 | C2×C3 | C22×C4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 304 | C2×C3 | C2×#4133 | 1 | 1 | yes | characteristic |
| 305 | C2×C3 | D5⋊#131 | 1 | 1 | yes | characteristic |
| 306 | C5 | Dic3×#131 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 307 | C22 | — | 5 | 6 | no | — |
| 308 | C22 | — | 10 | 3 | no | — |
| 309 | C22 | — | 10 | 3 | no | — |
| 310 | C22 | C22×D3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 311 | C4 | — | 3 | 2 | no | — |
| 312 | C4 | — | 5 | 1 | no | — |
| 313 | C4 | — | 5 | 1 | no | — |
| 314 | C4 | — | 6 | 3 | no | — |
| 315 | C4 | — | 15 | 2 | no | — |
| 316 | C4 | — | 30 | 3 | no | — |
| 317 | C4 | C2×Dic3×AGL(1,𝔽5) | 1 | 6 | yes | — |
| 318 | C3 | C4×#4133 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 319 | C2 | — | 10 | 6 | no | — |
| 320 | C2 | D3×#4133 | 1 | 1 | yes | characteristic |
| 321 | C2 | #11756849 | 1 | 1 | yes | characteristic |
| 322 | C2 | C22×Dic3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta