Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
405 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 405 conjugacy classes of subgroups — too many to draw. Only its 98 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. C3×#4834 | C2 | semidirect |
| 3. #10590338 | C2 | semidirect |
| 4. #10589349 | C2 | semidirect |
| 5. C3×#4480 | C2 | semidirect |
| 6. #10589080 | C2 | semidirect |
| 7. #10589079 | C2 | semidirect |
| 28. #4834 | D3 | semidirect |
| 37. #4480 | D3 | semidirect |
| 105. C3×D12 | M16 | semidirect |
| 226. D12 | ΓL(1,𝔽25) | semidirect |
| 313. C32 | #1586 | semidirect |
| 365. C3 | #68521 | semidirect |
| 366. C3 | #70844 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4834 | 2 |
| C4×#3714 | 2 |
| #10590338 | 2 |
| #10589349 | 2 |
| C3×#4480 | 2 |
| #10589080 | 2 |
| #10589079 | 2 |
| #70844 | 3 |
| #68521 | 3 |