Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
200 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10593729 | C2 | 1 | 3 | yes | maximal |
| 2 | C2×#3788 | C4 | 1 | 6 | yes | — |
| 3 | C42×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 4 | #63779 | — | 2 | 6 | no | — |
| 5 | C2×C4×C3⋊D3 | C2×C4 | 1 | 3 | yes | — |
| 6 | C2×#622 | — | 2 | 6 | no | — |
| 7 | #3788 | — | 4 | 6 | no | — |
| 8 | C32×C42 | Q8 | 1 | 1 | yes | characteristic |
| 9 | C4×C3⋊Dic3 | D4 | 1 | 3 | yes | — |
| 10 | #1309 | — | 9 | 1 | no | maximal, Sylow |
| 11 | C42×D3 | — | 12 | 1 | no | — |
| 12 | C22×C3⋊D3 | C42 | 1 | 1 | yes | characteristic |
| 13 | C2×C32×C4 | C4⋊C4 | 1 | 3 | yes | — |
| 14 | C2×C3⋊Dic3 | C22⋊C4 | 1 | 3 | yes | — |
| 15 | C4×C3⋊D3 | — | 2 | 3 | no | — |
| 16 | C4×C3⋊D3 | — | 2 | 3 | no | — |
| 17 | #622 | — | 4 | 6 | no | — |
| 18 | #423 | — | 9 | 3 | no | — |
| 19 | C2×C4×D3 | — | 12 | 3 | no | — |
| 20 | C3×C42 | — | 4 | 1 | no | — |
| 21 | C4×Dic3 | — | 12 | 3 | no | — |
| 22 | C22×C32 | #95 | 1 | 1 | yes | characteristic |
| 23 | C2×C3⋊D3 | — | 2 | 3 | no | — |
| 24 | C32×C4 | — | 2 | 3 | no | — |
| 25 | C3⋊Dic3 | #100 | 1 | 3 | yes | — |
| 26 | C3⋊Dic3 | #101 | 1 | 3 | yes | — |
| 27 | C2×M16 | — | 9 | 6 | no | — |
| 28 | C2×C42 | — | 9 | 1 | no | — |
| 29 | C4⋊C8 | — | 18 | 6 | no | — |
| 30 | C22×D3 | — | 12 | 1 | no | — |
| 31 | C2×C3×C4 | — | 4 | 3 | no | — |
| 32 | C2×Dic3 | — | 12 | 3 | no | — |
| 33 | C4×D3 | — | 12 | 6 | no | — |
| 34 | C4×D3 | — | 12 | 6 | no | — |
| 35 | C2×C32 | #343 | 1 | 3 | yes | — |
| 36 | C3⋊D3 | — | 4 | 1 | no | — |
| 37 | C22×C4 | — | 9 | 3 | no | — |
| 38 | M16 | — | 36 | 6 | no | — |
| 39 | C2×C8 | — | 18 | 6 | no | — |
| 40 | C42 | — | 9 | 3 | no | — |
| 41 | C42 | PSU(3,𝔽2) | 1 | 1 | yes | characteristic |
| 42 | C22×C3 | — | 4 | 1 | no | — |
| 43 | C2×D3 | — | 12 | 6 | no | — |
| 44 | C3×C4 | — | 4 | 6 | no | — |
| 45 | Dic3 | — | 12 | 3 | no | — |
| 46 | Dic3 | — | 12 | 3 | no | — |
| 47 | C32 | #1309 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 48 | C23 | — | 9 | 1 | no | — |
| 49 | C2×C4 | — | 9 | 3 | no | — |
| 50 | C2×C4 | — | 18 | 3 | no | — |
| 51 | C2×C4 | — | 18 | 3 | no | — |
| 52 | C2×C4 | #3777 | 1 | 3 | yes | — |
| 53 | C8 | — | 36 | 6 | no | — |
| 54 | C2×C3 | — | 4 | 3 | no | — |
| 55 | D3 | — | 12 | 4 | no | — |
| 56 | C22 | — | 18 | 3 | no | — |
| 57 | C22 | #63747 | 1 | 1 | yes | characteristic |
| 58 | C4 | — | 2 | 3 | no | — |
| 59 | C4 | — | 9 | 3 | no | — |
| 60 | C4 | — | 9 | 3 | no | — |
| 61 | C3 | — | 4 | 1 | no | — |
| 62 | C2 | — | 36 | 1 | no | — |
| 63 | C2 | #10590094 | 1 | 3 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 47. C32 | #1309 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593729 | 2 |
| #1309 | 9 |