Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
4854 conjugacy classes of subgroups; only the 807 normal subgroups are shown.
This group has 4854 conjugacy classes of subgroups — too many to draw. Only its 807 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C7×H(7,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11744348 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #11741570 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #11741569 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #11741555 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | C2×#90015 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #11741552 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C7×#585 | — | 2 | 12 | no | — |
| 9 | C7×#585 | C22 | 1 | 4 | yes | — |
| 10 | C2×C7×H(5,𝔽2) | — | 2 | 12 | no | — |
| 11 | C2×C7×H(5,𝔽2) | C22 | 1 | 8 | yes | — |
| 12 | C2×C7×H(5,𝔽2) | C22 | 1 | 3 | yes | — |
| 13 | C22×#1159 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | #90519 | C22 | 1 | 6 | yes | complemented |
| 15 | #90516 | C22 | 1 | 6 | yes | complemented |
| 16 | #90515 | — | 2 | 12 | no | — |
| 17 | #90497 | — | 2 | 12 | no | — |
| 18 | #90495 | C22 | 1 | 12 | yes | complemented |
| 19 | #90489 | C22 | 1 | 3 | yes | complemented |
| 20 | C2×#6498 | C22 | 1 | 12 | yes | complemented |
| 21 | #90016 | C22 | 1 | 16 | yes | complemented |
| 22 | #90015 | C22 | 1 | 16 | yes | complemented |
| 23 | #90015 | C22 | 1 | 32 | yes | complemented |
| 24 | #90012 | C22 | 1 | 12 | yes | complemented |
| 25 | C2×#6408 | C22 | 1 | 24 | yes | complemented |
| 26 | #60401 | — | 7 | 1 | no | maximal, Sylow |
| 27 | C7×2−1+4 | — | 2 | 16 | no | — |
| 28 | C7×2−1+4 | — | 2 | 12 | no | — |
| 29 | C7×H(5,𝔽2) | — | 2 | 48 | no | — |
| 30 | C7×H(5,𝔽2) | — | 2 | 12 | no | — |
| 31 | C7×H(5,𝔽2) | — | 2 | 48 | no | — |
| 32 | C7×H(5,𝔽2) | — | 2 | 24 | no | — |
| 33 | C7×H(5,𝔽2) | C23 | 1 | 16 | yes | — |
| 34 | C2×C7×#41 | — | 2 | 48 | no | — |
| 35 | C2×C7×#41 | — | 2 | 24 | no | — |
| 36 | C2×C7×#41 | — | 2 | 24 | no | — |
| 37 | C2×C7×#41 | D4 | 1 | 12 | yes | complemented |
| 38 | C2×C7×#41 | C23 | 1 | 6 | yes | — |
| 39 | C22×C7×D4 | — | 2 | 16 | no | — |
| 40 | C22×C7×D4 | — | 2 | 24 | no | — |
| 41 | C22×C7×D4 | D4 | 1 | 12 | yes | complemented |
| 42 | C22×C7×D4 | C23 | 1 | 12 | yes | — |
| 43 | C22×C7×D4 | C23 | 1 | 1 | yes | characteristic |
| 44 | C22×C22⋊D7 | C23 | 1 | 2 | yes | complemented |
| 45 | C23×Dic7 | C23 | 1 | 2 | yes | complemented |
| 46 | C2×#1159 | — | 2 | 12 | no | — |
| 47 | C22×C4×D7 | C23 | 1 | 1 | yes | characteristic, complemented |
| 48 | C22×Dic14 | C23 | 1 | 1 | yes | characteristic, complemented |
| 49 | #6516 | — | 2 | 12 | no | — |
| 50 | C2×C22⋊Dic7 | — | 2 | 12 | no | — |
| 51 | C2×C22⋊Dic7 | C23 | 1 | 12 | yes | complemented |
| 52 | #6509 | — | 2 | 6 | no | — |
| 53 | #6507 | — | 2 | 6 | no | — |
| 54 | #6502 | — | 2 | 24 | no | — |
| 55 | #6501 | — | 2 | 6 | no | — |
| 56 | #6500 | C23 | 1 | 12 | yes | complemented |
| 57 | #6499 | — | 2 | 6 | no | — |
| 58 | #6498 | — | 2 | 24 | no | — |
| 59 | #6498 | C23 | 1 | 12 | yes | complemented |
| 60 | #6498 | C23 | 1 | 24 | yes | complemented |
| 61 | D4×Dic7 | — | 2 | 12 | no | — |
| 62 | #6492 | — | 2 | 12 | no | — |
| 63 | C4×C22⋊D7 | — | 2 | 12 | no | — |
| 64 | #6489 | C23 | 1 | 6 | yes | complemented |
| 65 | #6487 | — | 2 | 12 | no | — |
| 66 | C2×Dic7⋊C4 | — | 2 | 12 | no | — |
| 67 | #6408 | C23 | 1 | 48 | yes | complemented |
| 68 | H(7,𝔽2) | D7 | 1 | 1 | yes | characteristic, complemented |
| 69 | #3485 | — | 7 | 3 | no | — |
| 70 | #3028 | — | 7 | 4 | no | — |
| 71 | #3026 | — | 7 | 8 | no | — |
| 72 | #3025 | — | 7 | 4 | no | — |
| 73 | C2×#458 | — | 7 | 8 | no | — |
| 74 | #2883 | — | 7 | 3 | no | — |
| 75 | C24×C7 | — | 2 | 8 | no | — |
| 76 | C24×C7 | C2×D4 | 1 | 12 | yes | — |
| 77 | C24×C7 | C24 | 1 | 2 | yes | — |
| 78 | C23×D7 | C24 | 1 | 1 | yes | characteristic |
| 79 | C7×#41 | — | 2 | 96 | no | — |
| 80 | C7×#41 | — | 2 | 48 | no | — |
| 81 | C7×#41 | — | 2 | 16 | no | — |
| 82 | C7×#41 | — | 2 | 48 | no | — |
| 83 | C7×#41 | — | 2 | 48 | no | — |
| 84 | C7×#41 | — | 2 | 24 | no | — |
| 85 | C2×C7×Q8 | — | 2 | 24 | no | — |
| 86 | C2×C7×Q8 | — | 2 | 8 | no | — |
| 87 | C2×C7×Q8 | C2×D4 | 1 | 6 | yes | — |
| 88 | C2×C7×D4 | — | 2 | 96 | no | — |
| 89 | C2×C7×D4 | — | 2 | 24 | no | — |
| 90 | C2×C7×D4 | — | 2 | 24 | no | — |
| 91 | C2×C7×D4 | — | 2 | 48 | no | — |
| 92 | C2×C7×D4 | — | 2 | 48 | no | — |
| 93 | C2×C7×D4 | — | 2 | 48 | no | — |
| 94 | C2×C7×D4 | C2×D4 | 1 | 24 | yes | — |
| 95 | C2×C7×D4 | C2×D4 | 1 | 6 | yes | — |
| 96 | C2×C7×D4 | C2×D4 | 1 | 12 | yes | — |
| 97 | C2×C7×D4 | C24 | 1 | 12 | yes | — |
| 98 | C22×C4×C7 | — | 2 | 24 | no | — |
| 99 | C22×C4×C7 | — | 2 | 16 | no | — |
| 100 | C22×C4×C7 | C2×D4 | 1 | 12 | yes | — |
| 101 | C22×C4×C7 | C2×D4 | 1 | 12 | yes | — |
| 102 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 103 | C2×C22⋊D7 | — | 2 | 12 | no | — |
| 104 | C2×C22⋊D7 | — | 2 | 12 | no | — |
| 105 | C22×Dic7 | — | 2 | 12 | no | — |
| 106 | C22×Dic7 | — | 2 | 12 | no | — |
| 107 | C22×Dic7 | C24 | 1 | 2 | yes | — |
| 108 | C22×Dic7 | C24 | 1 | 1 | yes | characteristic |
| 109 | #1159 | — | 4 | 16 | no | — |
| 110 | C2×C4×D7 | — | 2 | 6 | no | — |
| 111 | C2×Dic14 | — | 2 | 6 | no | — |
| 112 | C22⋊Dic7 | — | 2 | 24 | no | — |
| 113 | C22⋊Dic7 | — | 2 | 12 | no | — |
| 114 | C22⋊Dic7 | — | 2 | 12 | no | — |
| 115 | C22⋊Dic7 | C24 | 1 | 12 | yes | — |
| 116 | (C2×D7)⋊C4 | — | 2 | 12 | no | — |
| 117 | C4⋊Dic7 | — | 2 | 6 | no | — |
| 118 | Dic7⋊C4 | — | 2 | 12 | no | — |
| 119 | Dic7⋊C4 | — | 2 | 24 | no | — |
| 120 | C4×Dic7 | — | 2 | 6 | no | — |
| 121 | #585 | — | 2 | 12 | no | — |
| 122 | #585 | C2×D7 | 1 | 4 | yes | — |
| 123 | C2×H(5,𝔽2) | — | 2 | 12 | no | — |
| 124 | C2×H(5,𝔽2) | C2×D7 | 1 | 8 | yes | — |
| 125 | C2×H(5,𝔽2) | C2×D7 | 1 | 3 | yes | — |
| 126 | C22×#41 | — | 7 | 1 | no | — |
| 127 | #547 | — | 14 | 12 | no | — |
| 128 | #546 | — | 14 | 12 | no | — |
| 129 | #536 | — | 7 | 6 | no | — |
| 130 | #534 | — | 7 | 12 | no | — |
| 131 | #525 | — | 7 | 6 | no | — |
| 132 | C2×#123 | — | 7 | 12 | no | — |
| 133 | #518 | — | 7 | 3 | no | — |
| 134 | #458 | — | 7 | 16 | no | — |
| 135 | #458 | — | 7 | 32 | no | — |
| 136 | B(4,𝔽2) | — | 7 | 16 | no | — |
| 137 | #410 | — | 7 | 12 | no | — |
| 138 | C2×#99 | — | 7 | 24 | no | — |
| 139 | C23×C7 | — | 2 | 16 | no | — |
| 140 | C23×C7 | — | 2 | 24 | no | — |
| 141 | C23×C7 | — | 8 | 2 | no | — |
| 142 | C23×C7 | — | 8 | 12 | no | — |
| 143 | C23×C7 | — | 16 | 8 | no | — |
| 144 | C23×C7 | C22×D4 | 1 | 12 | yes | — |
| 145 | C23×C7 | C22×D4 | 1 | 12 | yes | — |
| 146 | C23×C7 | C25 | 1 | 1 | yes | characteristic |
| 147 | C22×D7 | — | 2 | 3 | no | — |
| 148 | C22×D7 | — | 8 | 1 | no | — |
| 149 | C7×Q8 | — | 2 | 16 | no | — |
| 150 | C7×Q8 | — | 2 | 12 | no | — |
| 151 | C7×D4 | — | 2 | 48 | no | — |
| 152 | C7×D4 | — | 2 | 48 | no | — |
| 153 | C7×D4 | — | 2 | 24 | no | — |
| 154 | C7×D4 | — | 2 | 12 | no | — |
| 155 | C7×D4 | #120 | 1 | 16 | yes | — |
| 156 | C2×C4×C7 | — | 2 | 48 | no | — |
| 157 | C2×C4×C7 | — | 2 | 24 | no | — |
| 158 | C2×C4×C7 | — | 2 | 24 | no | — |
| 159 | C2×C4×C7 | C22×D4 | 1 | 12 | yes | — |
| 160 | C2×C4×C7 | C22×D4 | 1 | 6 | yes | — |
| 161 | C22⋊D7 | — | 4 | 8 | no | — |
| 162 | C22⋊D7 | — | 8 | 12 | no | — |
| 163 | C2×Dic7 | — | 2 | 12 | no | — |
| 164 | C2×Dic7 | — | 2 | 6 | no | — |
| 165 | C2×Dic7 | — | 2 | 3 | no | — |
| 166 | C2×Dic7 | — | 4 | 8 | no | — |
| 167 | C2×Dic7 | — | 8 | 12 | no | — |
| 168 | C4×D7 | — | 4 | 4 | no | — |
| 169 | Dic14 | — | 4 | 4 | no | — |
| 170 | 2−1+4 | — | 2 | 16 | no | — |
| 171 | 2−1+4 | — | 2 | 12 | no | — |
| 172 | H(5,𝔽2) | — | 2 | 48 | no | — |
| 173 | H(5,𝔽2) | — | 2 | 12 | no | — |
| 174 | H(5,𝔽2) | — | 2 | 48 | no | — |
| 175 | H(5,𝔽2) | — | 2 | 24 | no | — |
| 176 | H(5,𝔽2) | C22×D7 | 1 | 16 | yes | — |
| 177 | C2×#41 | — | 2 | 48 | no | — |
| 178 | C2×#41 | — | 2 | 24 | no | — |
| 179 | C2×#41 | — | 2 | 24 | no | — |
| 180 | C2×#41 | — | 14 | 12 | no | — |
| 181 | C2×#41 | C22⋊D7 | 1 | 12 | yes | complemented |
| 182 | C2×#41 | C22×D7 | 1 | 6 | yes | — |
| 183 | C22×Q8 | — | 7 | 1 | no | — |
| 184 | C22×D4 | — | 2 | 16 | no | — |
| 185 | C22×D4 | — | 2 | 24 | no | — |
| 186 | C22×D4 | — | 7 | 2 | no | — |
| 187 | C22×D4 | C22⋊D7 | 1 | 12 | yes | complemented |
| 188 | C22×D4 | C22×D7 | 1 | 12 | yes | — |
| 189 | C22×D4 | C22×D7 | 1 | 1 | yes | characteristic |
| 190 | C23×C4 | — | 7 | 2 | no | — |
| 191 | C23×C4 | — | 7 | 1 | no | — |
| 192 | C4⋊Q8 | — | 14 | 6 | no | — |
| 193 | #124 | — | 14 | 6 | no | — |
| 194 | #123 | — | 7 | 12 | no | — |
| 195 | #123 | — | 7 | 24 | no | — |
| 196 | #123 | — | 14 | 24 | no | — |
| 197 | #123 | — | 14 | 12 | no | — |
| 198 | C22⋊Q8 | — | 14 | 6 | no | — |
| 199 | C22⋊Q8 | — | 14 | 12 | no | — |
| 200 | #121 | — | 14 | 6 | no | — |
| 201 | #121 | — | 14 | 24 | no | — |
| 202 | #120 | — | 7 | 12 | no | — |
| 203 | #120 | — | 14 | 12 | no | — |
| 204 | C4×D4 | — | 14 | 12 | no | — |
| 205 | C4×D4 | — | 14 | 12 | no | — |
| 206 | #117 | — | 7 | 6 | no | — |
| 207 | C2×C4⋊C4 | — | 14 | 12 | no | — |
| 208 | C2×C22⋊C4 | — | 7 | 12 | no | — |
| 209 | C2×C22⋊C4 | — | 14 | 12 | no | — |
| 210 | #99 | — | 7 | 48 | no | — |
| 211 | C22×C7 | — | 2 | 12 | no | — |
| 212 | C22×C7 | — | 4 | 12 | no | — |
| 213 | C22×C7 | — | 4 | 1 | no | — |
| 214 | C22×C7 | — | 4 | 12 | no | — |
| 215 | C22×C7 | — | 8 | 24 | no | — |
| 216 | C22×C7 | — | 8 | 16 | no | — |
| 217 | C22×C7 | C2×#120 | 1 | 8 | yes | — |
| 218 | C22×C7 | C23×D4 | 1 | 3 | yes | — |
| 219 | C2×D7 | — | 4 | 6 | no | — |
| 220 | C2×D7 | — | 4 | 1 | no | — |
| 221 | C4×C7 | — | 2 | 12 | no | — |
| 222 | C4×C7 | C2×#120 | 1 | 4 | yes | — |
| 223 | Dic7 | — | 4 | 12 | no | — |
| 224 | Dic7 | — | 4 | 2 | no | — |
| 225 | Dic7 | — | 4 | 1 | no | — |
| 226 | C24 | — | 2 | 8 | no | — |
| 227 | C24 | — | 7 | 1 | no | — |
| 228 | C24 | C2×C22⋊D7 | 1 | 12 | yes | — |
| 229 | C24 | C23×D7 | 1 | 2 | yes | — |
| 230 | #41 | — | 2 | 96 | no | — |
| 231 | #41 | — | 2 | 48 | no | — |
| 232 | #41 | — | 2 | 16 | no | — |
| 233 | #41 | — | 2 | 48 | no | — |
| 234 | #41 | — | 2 | 48 | no | — |
| 235 | #41 | — | 2 | 24 | no | — |
| 236 | #41 | — | 28 | 16 | no | — |
| 237 | C2×Q8 | — | 2 | 24 | no | — |
| 238 | C2×Q8 | — | 2 | 8 | no | — |
| 239 | C2×Q8 | — | 14 | 6 | no | — |
| 240 | C2×Q8 | C2×C22⋊D7 | 1 | 6 | yes | — |
| 241 | C2×D4 | — | 2 | 96 | no | — |
| 242 | C2×D4 | — | 2 | 24 | no | — |
| 243 | C2×D4 | — | 2 | 24 | no | — |
| 244 | C2×D4 | — | 2 | 48 | no | — |
| 245 | C2×D4 | — | 2 | 48 | no | — |
| 246 | C2×D4 | — | 2 | 48 | no | — |
| 247 | C2×D4 | — | 14 | 12 | no | — |
| 248 | C2×D4 | — | 14 | 12 | no | — |
| 249 | C2×D4 | C2×C22⋊D7 | 1 | 24 | yes | — |
| 250 | C2×D4 | C2×C22⋊D7 | 1 | 6 | yes | — |
| 251 | C2×D4 | C2×C22⋊D7 | 1 | 12 | yes | — |
| 252 | C2×D4 | C23×D7 | 1 | 12 | yes | — |
| 253 | C22×C4 | — | 2 | 24 | no | — |
| 254 | C22×C4 | — | 2 | 16 | no | — |
| 255 | C22×C4 | — | 7 | 1 | no | — |
| 256 | C22×C4 | — | 7 | 2 | no | — |
| 257 | C22×C4 | — | 14 | 12 | no | — |
| 258 | C22×C4 | — | 14 | 12 | no | — |
| 259 | C22×C4 | — | 14 | 6 | no | — |
| 260 | C22×C4 | C2×C22⋊D7 | 1 | 12 | yes | — |
| 261 | C22×C4 | C2×C22⋊D7 | 1 | 12 | yes | — |
| 262 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 263 | C4⋊C4 | — | 14 | 12 | no | — |
| 264 | C4⋊C4 | — | 14 | 24 | no | — |
| 265 | C4⋊C4 | — | 14 | 6 | no | — |
| 266 | C22⋊C4 | — | 7 | 12 | no | — |
| 267 | C22⋊C4 | — | 14 | 12 | no | — |
| 268 | C22⋊C4 | — | 14 | 12 | no | — |
| 269 | C22⋊C4 | — | 14 | 24 | no | — |
| 270 | C22⋊C4 | — | 14 | 12 | no | — |
| 271 | C42 | — | 14 | 6 | no | — |
| 272 | C2×C7 | — | 2 | 3 | no | — |
| 273 | C2×C7 | — | 2 | 8 | no | — |
| 274 | C2×C7 | — | 4 | 12 | no | — |
| 275 | C2×C7 | C22×#120 | 1 | 1 | yes | characteristic |
| 276 | D7 | — | 8 | 1 | no | — |
| 277 | C23 | — | 2 | 16 | no | — |
| 278 | C23 | — | 2 | 24 | no | — |
| 279 | C23 | — | 8 | 2 | no | — |
| 280 | C23 | — | 8 | 12 | no | — |
| 281 | C23 | — | 14 | 3 | no | — |
| 282 | C23 | — | 16 | 8 | no | — |
| 283 | C23 | — | 56 | 1 | no | — |
| 284 | C23 | C22×C22⋊D7 | 1 | 12 | yes | — |
| 285 | C23 | C22×C22⋊D7 | 1 | 12 | yes | — |
| 286 | C23 | C24×D7 | 1 | 1 | yes | characteristic |
| 287 | Q8 | — | 2 | 16 | no | — |
| 288 | Q8 | — | 2 | 12 | no | — |
| 289 | Q8 | — | 28 | 4 | no | — |
| 290 | D4 | — | 2 | 48 | no | — |
| 291 | D4 | — | 2 | 48 | no | — |
| 292 | D4 | — | 2 | 24 | no | — |
| 293 | D4 | — | 2 | 12 | no | — |
| 294 | D4 | — | 28 | 8 | no | — |
| 295 | D4 | — | 56 | 12 | no | — |
| 296 | D4 | #6516 | 1 | 16 | yes | — |
| 297 | C2×C4 | — | 2 | 48 | no | — |
| 298 | C2×C4 | — | 2 | 24 | no | — |
| 299 | C2×C4 | — | 2 | 24 | no | — |
| 300 | C2×C4 | — | 14 | 12 | no | — |
| 301 | C2×C4 | — | 14 | 3 | no | — |
| 302 | C2×C4 | — | 14 | 6 | no | — |
| 303 | C2×C4 | — | 28 | 8 | no | — |
| 304 | C2×C4 | — | 28 | 4 | no | — |
| 305 | C2×C4 | — | 56 | 12 | no | — |
| 306 | C2×C4 | C22×C22⋊D7 | 1 | 12 | yes | — |
| 307 | C2×C4 | C22×C22⋊D7 | 1 | 6 | yes | — |
| 308 | C7 | #60401 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 309 | C22 | — | 2 | 12 | no | — |
| 310 | C22 | — | 4 | 12 | no | — |
| 311 | C22 | — | 4 | 1 | no | — |
| 312 | C22 | — | 4 | 12 | no | — |
| 313 | C22 | — | 8 | 24 | no | — |
| 314 | C22 | — | 8 | 16 | no | — |
| 315 | C22 | — | 28 | 6 | no | — |
| 316 | C22 | — | 28 | 1 | no | — |
| 317 | C22 | C2×#6516 | 1 | 8 | yes | — |
| 318 | C22 | C23×C22⋊D7 | 1 | 3 | yes | — |
| 319 | C4 | — | 2 | 12 | no | — |
| 320 | C4 | — | 28 | 12 | no | — |
| 321 | C4 | — | 28 | 1 | no | — |
| 322 | C4 | — | 28 | 2 | no | — |
| 323 | C4 | C2×#6516 | 1 | 4 | yes | — |
| 324 | C2 | — | 2 | 3 | no | — |
| 325 | C2 | — | 2 | 8 | no | — |
| 326 | C2 | — | 4 | 12 | no | — |
| 327 | C2 | — | 56 | 1 | no | — |
| 328 | C2 | C22×#6516 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×H(7,𝔽2) | C2 | semidirect |
| 2. #11744348 | C2 | semidirect |
| 3. #11741570 | C2 | semidirect |
| 4. #11741569 | C2 | semidirect |
| 5. #11741555 | C2 | semidirect |
| 6. C2×#90015 | C2 | semidirect |
| 7. #11741552 | C2 | semidirect |
| 13. C22×#1159 | C22 | semidirect |
| 14. #90519 | C22 | semidirect |
| 15. #90516 | C22 | semidirect |
| 18. #90495 | C22 | semidirect |
| 19. #90489 | C22 | semidirect |
| 20. C2×#6498 | C22 | semidirect |
| 21. #90016 | C22 | semidirect |
| 22. #90015 | C22 | semidirect |
| 23. #90015 | C22 | semidirect |
| 24. #90012 | C22 | semidirect |
| 25. C2×#6408 | C22 | semidirect |
| 37. C2×C7×#41 | D4 | semidirect |
| 41. C22×C7×D4 | D4 | semidirect |
| 44. C22×C22⋊D7 | C23 | semidirect |
| 45. C23×Dic7 | C23 | semidirect |
| 47. C22×C4×D7 | C23 | semidirect |
| 48. C22×Dic14 | C23 | semidirect |
| 51. C2×C22⋊Dic7 | C23 | semidirect |
| 56. #6500 | C23 | semidirect |
| 59. #6498 | C23 | semidirect |
| 60. #6498 | C23 | semidirect |
| 64. #6489 | C23 | semidirect |
| 67. #6408 | C23 | semidirect |
| 68. H(7,𝔽2) | D7 | semidirect |
| 181. C2×#41 | C22⋊D7 | semidirect |
| 187. C22×D4 | C22⋊D7 | semidirect |
| 308. C7 | #60401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×H(7,𝔽2) | 2 |
| #11744348 | 2 |
| #11741570 | 2 |
| #11741569 | 2 |
| #11741555 | 2 |
| C2×#90015 | 2 |
| #11741552 | 2 |
| #60401 | 7 |