Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
385 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 385 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 |
|---|---|---|
| 3. C3×#4466 | C2 | semidirect |
| 4. #10589106 | C2 | semidirect |
| 14. #63544 | C4 | semidirect |
| 15. #63542 | C4 | semidirect |
| 21. #4466 | D3 | semidirect |
| 170. C32 | #2110 | semidirect |
| 198. C3 | #69087 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592407 | 2 |
| #10590625 | 2 |
| C3×#4466 | 2 |
| #10589106 | 2 |
| #69087 | 3 |