Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
231 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 231 conjugacy classes of subgroups — too many to draw. Only its 48 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 | #10592412 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×#4466 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #67520 | — | 3 | 2 | no | maximal |
| 4 | #64083 | C4 | 1 | 1 | yes | characteristic |
| 5 | #64079 | C4 | 1 | 1 | yes | characteristic |
| 6 | C32×#97 | C22 | 1 | 1 | yes | characteristic |
| 7 | #63648 | — | 2 | 2 | no | — |
| 8 | C3×#812 | — | 2 | 2 | no | — |
| 9 | #4713 | — | 3 | 2 | no | — |
| 10 | #4713 | — | 6 | 1 | no | — |
| 11 | C3×#347 | — | 3 | 2 | no | — |
| 12 | #4466 | D3 | 1 | 2 | yes | complemented |
| 13 | C2×C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 14 | C2×C4⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 15 | C2×C32×C8 | D4 | 1 | 2 | yes | — |
| 16 | C32×C42 | C2×C4 | 1 | 1 | yes | characteristic |
| 17 | C4⋊(C3⋊Dic3) | — | 2 | 1 | no | — |
| 18 | #3750 | — | 4 | 1 | no | — |
| 19 | C3×C3⋊C16 | — | 2 | 4 | no | — |
| 20 | #1355 | — | 9 | 1 | no | Sylow |
| 21 | #874 | — | 3 | 2 | no | — |
| 22 | #874 | — | 6 | 1 | no | — |
| 23 | #870 | — | 3 | 2 | no | — |
| 24 | #870 | — | 6 | 1 | no | — |
| 25 | C3×M32 | — | 6 | 2 | no | — |
| 26 | C3×#97 | — | 2 | 1 | no | — |
| 27 | C3×#97 | C2×D3 | 1 | 2 | yes | — |
| 28 | #821 | — | 6 | 4 | no | — |
| 29 | #821 | — | 6 | 2 | no | — |
| 30 | #821 | — | 6 | 2 | no | — |
| 31 | #812 | — | 2 | 2 | no | — |
| 32 | C22×C3⋊D3 | — | 4 | 1 | no | — |
| 33 | C2×C32×C4 | — | 2 | 1 | no | — |
| 34 | C2×C32×C4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 35 | C2×C3⋊Dic3 | — | 4 | 1 | no | — |
| 36 | C4⋊(C3⋊D3) | — | 4 | 2 | no | — |
| 37 | C4⋊(C3⋊D3) | — | 8 | 2 | no | — |
| 38 | C32×C8 | — | 2 | 2 | no | — |
| 39 | #490 | — | 9 | 1 | no | — |
| 40 | #347 | — | 3 | 2 | no | — |
| 41 | C2×D12 | — | 6 | 2 | no | — |
| 42 | C2×D12 | — | 6 | 2 | no | — |
| 43 | C2×D12 | — | 12 | 2 | no | — |
| 44 | C2×D12 | — | 12 | 2 | no | — |
| 45 | C2×C3×C8 | — | 2 | 2 | no | — |
| 46 | C2×C3×C8 | D12 | 1 | 2 | yes | — |
| 47 | C2×C3×C8 | #67 | 1 | 2 | yes | — |
| 48 | C3×C42 | — | 2 | 1 | no | — |
| 49 | C3×C42 | C4×D3 | 1 | 2 | yes | — |
| 50 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 51 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 52 | Dic3⋊C4 | — | 12 | 2 | no | — |
| 53 | Dic3⋊C4 | — | 12 | 2 | no | — |
| 54 | C3×C16 | — | 6 | 4 | no | — |
| 55 | C3⋊C16 | — | 2 | 4 | no | — |
| 56 | C22×C32 | #100 | 1 | 1 | yes | characteristic |
| 57 | C2×C3⋊D3 | — | 8 | 2 | no | — |
| 58 | C2×C3⋊D3 | — | 8 | 1 | no | — |
| 59 | C32×C4 | — | 4 | 1 | no | — |
| 60 | C32×C4 | #104 | 1 | 2 | yes | — |
| 61 | C3⋊Dic3 | — | 8 | 1 | no | — |
| 62 | #127 | — | 9 | 1 | no | — |
| 63 | #125 | — | 9 | 1 | no | — |
| 64 | M32 | — | 6 | 2 | no | — |
| 65 | #102 | — | 18 | 2 | no | — |
| 66 | #97 | D32 | 1 | 1 | yes | characteristic |
| 67 | C22×D3 | — | 12 | 2 | no | — |
| 68 | C22×D3 | — | 12 | 2 | no | — |
| 69 | C2×C3×C4 | — | 2 | 2 | no | — |
| 70 | C2×C3×C4 | — | 2 | 2 | no | — |
| 71 | C2×C3×C4 | — | 2 | 1 | no | — |
| 72 | C2×C3×C4 | (C2×D3)⋊C4 | 1 | 2 | yes | — |
| 73 | C2×Dic3 | — | 12 | 2 | no | — |
| 74 | C2×Dic3 | — | 12 | 2 | no | — |
| 75 | D12 | — | 12 | 4 | no | — |
| 76 | D12 | — | 12 | 2 | no | — |
| 77 | D12 | — | 12 | 2 | no | — |
| 78 | D12 | — | 24 | 4 | no | — |
| 79 | D12 | — | 24 | 4 | no | — |
| 80 | C3×C8 | — | 2 | 2 | no | — |
| 81 | C3×C8 | — | 2 | 2 | no | — |
| 82 | C3×C8 | — | 4 | 2 | no | — |
| 83 | C2×C32 | — | 2 | 1 | no | — |
| 84 | C2×C32 | #329 | 1 | 1 | yes | characteristic |
| 85 | C3⋊D3 | — | 16 | 1 | no | — |
| 86 | C2×D4 | — | 18 | 1 | no | — |
| 87 | C2×D4 | — | 36 | 1 | no | — |
| 88 | C2×C8 | #626 | 1 | 2 | yes | — |
| 89 | C4⋊C4 | — | 18 | 1 | no | — |
| 90 | C4⋊C4 | — | 36 | 1 | no | — |
| 91 | C42 | #624 | 1 | 1 | yes | characteristic |
| 92 | C16 | — | 6 | 4 | no | — |
| 93 | C22×C3 | — | 2 | 1 | no | — |
| 94 | C22×C3 | #823 | 1 | 2 | yes | — |
| 95 | C2×D3 | — | 24 | 2 | no | — |
| 96 | C2×D3 | — | 24 | 4 | no | — |
| 97 | C2×D3 | — | 24 | 4 | no | — |
| 98 | C2×D3 | — | 24 | 2 | no | — |
| 99 | C3×C4 | — | 2 | 2 | no | — |
| 100 | C3×C4 | — | 4 | 2 | no | — |
| 101 | C3×C4 | — | 4 | 2 | no | — |
| 102 | C3×C4 | #805 | 1 | 2 | yes | — |
| 103 | C3×C4 | #825 | 1 | 2 | yes | — |
| 104 | Dic3 | — | 24 | 2 | no | — |
| 105 | Dic3 | — | 24 | 2 | no | — |
| 106 | C32 | #1355 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 107 | C23 | — | 36 | 1 | no | — |
| 108 | D4 | — | 36 | 2 | no | — |
| 109 | D4 | — | 72 | 2 | no | — |
| 110 | C2×C4 | — | 2 | 1 | no | — |
| 111 | C2×C4 | — | 36 | 1 | no | — |
| 112 | C2×C4 | #3722 | 1 | 1 | yes | characteristic |
| 113 | C8 | — | 2 | 2 | no | — |
| 114 | C2×C3 | — | 2 | 2 | no | — |
| 115 | C2×C3 | — | 2 | 2 | no | — |
| 116 | C2×C3 | — | 2 | 1 | no | — |
| 117 | C2×C3 | #4464 | 1 | 2 | yes | — |
| 118 | D3 | — | 48 | 2 | no | — |
| 119 | D3 | — | 48 | 2 | no | — |
| 120 | C22 | — | 72 | 2 | no | — |
| 121 | C22 | — | 72 | 1 | no | — |
| 122 | C22 | #63559 | 1 | 1 | yes | characteristic |
| 123 | C4 | — | 4 | 1 | no | — |
| 124 | C4 | — | 72 | 1 | no | — |
| 125 | C4 | #63570 | 1 | 2 | yes | — |
| 126 | C3 | — | 2 | 1 | no | — |
| 127 | C3 | #67520 | 1 | 2 | yes | complemented |
| 128 | C2 | — | 2 | 1 | no | — |
| 129 | C2 | — | 144 | 1 | no | — |
| 130 | C2 | #10589087 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#4466 | C2 | semidirect |
| 12. #4466 | D3 | semidirect |
| 106. C32 | #1355 | semidirect |
| 127. C3 | #67520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592412 | 2 |
| C3×#4466 | 2 |
| #67520 | 3 |