Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
222 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 30 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 | #11763687 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11763653 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11762719 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C22×D68 | — | 2 | 1 | no | — |
| 5 | C22×D68 | C4 | 1 | 1 | yes | characteristic, complemented |
| 6 | C2×C22⋊#595 | — | 2 | 1 | no | — |
| 7 | C2×#63227 | — | 2 | 1 | no | — |
| 8 | C2×#63227 | C22 | 1 | 1 | yes | characteristic |
| 9 | C22⋊#3624 | — | 2 | 1 | no | — |
| 10 | C17×#95 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | C23×D17 | — | 2 | 1 | no | — |
| 12 | C23×D17 | D4 | 1 | 1 | yes | characteristic |
| 13 | C22×#595 | — | 4 | 1 | no | — |
| 14 | C22×C4×C17 | — | 2 | 1 | no | — |
| 15 | C22×C4×C17 | C2×C4 | 1 | 1 | yes | characteristic |
| 16 | C22×Dic17 | D4 | 1 | 1 | yes | characteristic |
| 17 | C2×D68 | — | 4 | 1 | no | — |
| 18 | C2×D68 | — | 4 | 2 | no | — |
| 19 | C2×D68 | — | 4 | 2 | no | — |
| 20 | C2×D68 | — | 4 | 1 | no | — |
| 21 | C2×D68 | — | 4 | 1 | no | — |
| 22 | C2×D68 | — | 4 | 2 | no | — |
| 23 | C22⋊#595 | — | 2 | 2 | no | — |
| 24 | C22⋊#595 | — | 4 | 1 | no | — |
| 25 | C2×#3624 | — | 4 | 1 | no | — |
| 26 | #63227 | — | 4 | 1 | no | — |
| 27 | #63227 | — | 4 | 2 | no | — |
| 28 | C23×C17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 29 | C22×D17 | — | 2 | 1 | no | — |
| 30 | C22×D17 | — | 2 | 1 | no | — |
| 31 | C22×D17 | — | 2 | 2 | no | — |
| 32 | C22×D17 | — | 4 | 1 | no | — |
| 33 | C22×D17 | — | 4 | 1 | no | — |
| 34 | C22×D17 | — | 4 | 1 | no | — |
| 35 | C22×D17 | — | 4 | 1 | no | — |
| 36 | C22×D17 | — | 4 | 1 | no | — |
| 37 | C22×D17 | — | 4 | 1 | no | — |
| 38 | C22×D17 | — | 4 | 1 | no | — |
| 39 | C22×D17 | — | 4 | 1 | no | — |
| 40 | C22×D17 | D8 | 1 | 1 | yes | characteristic |
| 41 | C22×D17 | SD16 | 1 | 1 | yes | characteristic |
| 42 | C2×#595 | — | 4 | 2 | no | — |
| 43 | C2×#595 | — | 8 | 1 | no | — |
| 44 | C2×#595 | — | 8 | 1 | no | — |
| 45 | C2×C4×C17 | — | 2 | 2 | no | — |
| 46 | C2×C4×C17 | — | 2 | 1 | no | — |
| 47 | C2×C4×C17 | — | 4 | 1 | no | — |
| 48 | C2×C4×C17 | — | 4 | 1 | no | — |
| 49 | C2×C4×C17 | — | 4 | 1 | no | — |
| 50 | C2×Dic17 | — | 2 | 1 | no | — |
| 51 | C2×Dic17 | — | 4 | 1 | no | — |
| 52 | D68 | — | 4 | 2 | no | — |
| 53 | D68 | — | 4 | 4 | no | — |
| 54 | D68 | — | 4 | 4 | no | — |
| 55 | D68 | — | 4 | 2 | no | — |
| 56 | #3624 | — | 8 | 1 | no | — |
| 57 | #1343 | — | 17 | 1 | no | maximal, Sylow |
| 58 | C22×C17 | — | 2 | 1 | no | — |
| 59 | C22×C17 | — | 2 | 1 | no | — |
| 60 | C22×C17 | #99 | 1 | 1 | yes | characteristic |
| 61 | C22×C17 | #102 | 1 | 1 | yes | characteristic |
| 62 | C22×C17 | #104 | 1 | 1 | yes | characteristic |
| 63 | C2×D17 | — | 2 | 1 | no | — |
| 64 | C2×D17 | — | 2 | 1 | no | — |
| 65 | C2×D17 | — | 4 | 1 | no | — |
| 66 | C2×D17 | — | 4 | 1 | no | — |
| 67 | C2×D17 | — | 4 | 1 | no | — |
| 68 | C2×D17 | — | 4 | 1 | no | — |
| 69 | C2×D17 | — | 4 | 2 | no | — |
| 70 | C2×D17 | — | 4 | 2 | no | — |
| 71 | C2×D17 | — | 4 | 2 | no | — |
| 72 | C2×D17 | — | 8 | 1 | no | — |
| 73 | C2×D17 | — | 8 | 1 | no | — |
| 74 | C2×D17 | — | 8 | 1 | no | — |
| 75 | C2×D17 | — | 8 | 1 | no | — |
| 76 | C2×D17 | — | 8 | 1 | no | — |
| 77 | #595 | — | 8 | 2 | no | — |
| 78 | C4×C17 | — | 4 | 2 | no | — |
| 79 | C4×C17 | — | 4 | 1 | no | — |
| 80 | Dic17 | — | 4 | 1 | no | — |
| 81 | #392 | — | 17 | 1 | no | — |
| 82 | #342 | — | 17 | 1 | no | — |
| 83 | #323 | — | 17 | 1 | no | — |
| 84 | C2×C17 | — | 2 | 1 | no | — |
| 85 | C2×C17 | — | 2 | 1 | no | — |
| 86 | C2×C17 | #327 | 1 | 1 | yes | characteristic |
| 87 | C2×C17 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 88 | C2×C17 | #353 | 1 | 1 | yes | characteristic |
| 89 | D17 | — | 4 | 1 | no | — |
| 90 | D17 | — | 4 | 1 | no | — |
| 91 | D17 | — | 8 | 2 | no | — |
| 92 | C22×D4 | — | 17 | 1 | no | — |
| 93 | C22×D4 | — | 34 | 1 | no | — |
| 94 | C2×C22⋊C4 | — | 17 | 1 | no | — |
| 95 | C2×C22⋊C4 | — | 34 | 1 | no | — |
| 96 | C2×C22⋊C4 | — | 34 | 1 | no | — |
| 97 | C22⋊C8 | — | 34 | 1 | no | — |
| 98 | #95 | #595 | 1 | 1 | yes | characteristic, complemented |
| 99 | C17 | #1343 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 100 | C24 | — | 17 | 1 | no | — |
| 101 | C24 | — | 34 | 1 | no | — |
| 102 | C2×D4 | — | 68 | 1 | no | — |
| 103 | C2×D4 | — | 68 | 2 | no | — |
| 104 | C2×D4 | — | 68 | 1 | no | — |
| 105 | C2×D4 | — | 68 | 1 | no | — |
| 106 | C2×D4 | — | 68 | 2 | no | — |
| 107 | C2×D4 | — | 68 | 2 | no | — |
| 108 | C22×C4 | — | 2 | 1 | no | — |
| 109 | C22×C4 | — | 17 | 1 | no | — |
| 110 | C22×C4 | — | 68 | 1 | no | — |
| 111 | C22×C4 | C2×#595 | 1 | 1 | yes | characteristic |
| 112 | C2×C8 | — | 68 | 1 | no | — |
| 113 | C22⋊C4 | — | 34 | 2 | no | — |
| 114 | C22⋊C4 | — | 68 | 1 | no | — |
| 115 | C22⋊C4 | — | 68 | 2 | no | — |
| 116 | C22⋊C4 | — | 68 | 1 | no | — |
| 117 | C23 | — | 17 | 1 | no | — |
| 118 | C23 | — | 17 | 1 | no | — |
| 119 | C23 | — | 34 | 2 | no | — |
| 120 | C23 | — | 34 | 1 | no | — |
| 121 | C23 | — | 34 | 1 | no | — |
| 122 | C23 | — | 68 | 1 | no | — |
| 123 | C23 | — | 68 | 1 | no | — |
| 124 | C23 | — | 68 | 1 | no | — |
| 125 | C23 | — | 68 | 1 | no | — |
| 126 | C23 | — | 68 | 1 | no | — |
| 127 | C23 | — | 68 | 1 | no | — |
| 128 | C23 | — | 68 | 1 | no | — |
| 129 | C23 | — | 68 | 1 | no | — |
| 130 | C23 | C22⋊#595 | 1 | 1 | yes | characteristic |
| 131 | D4 | — | 68 | 2 | no | — |
| 132 | D4 | — | 68 | 4 | no | — |
| 133 | D4 | — | 68 | 4 | no | — |
| 134 | D4 | — | 68 | 2 | no | — |
| 135 | C2×C4 | — | 2 | 2 | no | — |
| 136 | C2×C4 | — | 2 | 1 | no | — |
| 137 | C2×C4 | — | 4 | 1 | no | — |
| 138 | C2×C4 | — | 4 | 1 | no | — |
| 139 | C2×C4 | — | 4 | 1 | no | — |
| 140 | C2×C4 | — | 34 | 1 | no | — |
| 141 | C2×C4 | — | 68 | 1 | no | — |
| 142 | C2×C4 | — | 68 | 2 | no | — |
| 143 | C2×C4 | — | 136 | 1 | no | — |
| 144 | C2×C4 | — | 136 | 1 | no | — |
| 145 | C8 | — | 136 | 1 | no | — |
| 146 | C22 | — | 2 | 1 | no | — |
| 147 | C22 | — | 2 | 1 | no | — |
| 148 | C22 | — | 34 | 1 | no | — |
| 149 | C22 | — | 34 | 1 | no | — |
| 150 | C22 | — | 68 | 1 | no | — |
| 151 | C22 | — | 68 | 1 | no | — |
| 152 | C22 | — | 68 | 2 | no | — |
| 153 | C22 | — | 68 | 2 | no | — |
| 154 | C22 | — | 68 | 1 | no | — |
| 155 | C22 | — | 68 | 1 | no | — |
| 156 | C22 | — | 68 | 2 | no | — |
| 157 | C22 | — | 136 | 1 | no | — |
| 158 | C22 | — | 136 | 1 | no | — |
| 159 | C22 | — | 136 | 1 | no | — |
| 160 | C22 | — | 136 | 1 | no | — |
| 161 | C22 | — | 136 | 1 | no | — |
| 162 | C22 | #10587539 | 1 | 1 | yes | characteristic |
| 163 | C22 | #10587547 | 1 | 1 | yes | characteristic |
| 164 | C22 | #10587550 | 1 | 1 | yes | characteristic |
| 165 | C4 | — | 4 | 2 | no | — |
| 166 | C4 | — | 4 | 1 | no | — |
| 167 | C4 | — | 68 | 1 | no | — |
| 168 | C4 | — | 136 | 2 | no | — |
| 169 | C2 | — | 2 | 1 | no | — |
| 170 | C2 | — | 2 | 1 | no | — |
| 171 | C2 | — | 68 | 1 | no | — |
| 172 | C2 | — | 68 | 1 | no | — |
| 173 | C2 | — | 136 | 2 | no | — |
| 174 | C2 | #11763661 | 1 | 1 | yes | characteristic |
| 175 | C2 | #11763710 | 1 | 1 | yes | characteristic |
| 176 | C2 | #11763714 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11763687 | C2 | semidirect |
| 2. #11763653 | C2 | semidirect |
| 5. C22×D68 | C4 | semidirect |
| 10. C17×#95 | C4 | semidirect |
| 98. #95 | #595 | semidirect |
| 99. C17 | #1343 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763687 | 2 |
| #11763653 | 2 |
| #11762719 | 2 |
| #1343 | 17 |