Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
457 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 457 conjugacy classes of subgroups — too many to draw. Only its 116 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. #10592398 | C2 | semidirect |
| 3. #10590311 | C2 | semidirect |
| 5. C3×#4455 | C2 | semidirect |
| 27. #4455 | D3 | semidirect |
| 184. C32 | #1722 | semidirect |
| 212. C3 | #68098 | semidirect |
| 213. C3 | #71263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592398 | 2 |
| C3×#4693 | 2 |
| #10590311 | 2 |
| #10590273 | 2 |
| C3×#4455 | 2 |
| #71263 | 3 |
| #68098 | 3 |