Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1530 conjugacy classes of subgroups; only the 263 normal subgroups are shown.
This group has 1530 conjugacy classes of subgroups — too many to draw. Only its 263 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#3745 | C2 | semidirect |
| 2. C2×#64083 | C2 | semidirect |
| 3. C2×#63648 | C2 | semidirect |
| 4. #10592638 | C2 | semidirect |
| 5. C32×#336 | C2 | semidirect |
| 23. C3×#336 | D3 | semidirect |
| 41. C2×C4⋊(C3⋊D3) | D4 | semidirect |
| 44. C2×C32×C8 | D4 | semidirect |
| 75. C2×C32×C4 | D8 | semidirect |
| 94. #336 | C3⋊D3 | semidirect |
| 115. C2×C3×C8 | D12 | semidirect |
| 164. C2×C3×C4 | D24 | semidirect |
| 207. C2×C8 | C4⋊(C3⋊D3) | semidirect |
| 230. C32 | #2011 | semidirect |
| 253. C2×C4 | #3745 | semidirect |
| 285. C3 | #68674 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3745 | 2 |
| C2×#64083 | 2 |
| C2×#63648 | 2 |
| #10592638 | 2 |
| C32×#336 | 2 |
| #68674 | 3 |