Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
365 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 365 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 |
|---|---|---|
| 4. C3×#4512 | C2 | semidirect |
| 5. #10589105 | C2 | semidirect |
| 12. #63625 | C4 | semidirect |
| 13. C16×C3⋊D3 | C4 | semidirect |
| 17. #63544 | C4 | semidirect |
| 18. #63542 | C4 | semidirect |
| 25. #4512 | D3 | semidirect |
| 195. C32 | #2110 | semidirect |
| 227. C3 | #69087 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×M32 | 2 |
| #10590703 | 2 |
| #10590625 | 2 |
| C3×#4512 | 2 |
| #10589105 | 2 |
| #69087 | 3 |