Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
393 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 393 conjugacy classes of subgroups — too many to draw. Only its 82 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. C2×#63627 | C2 | semidirect |
| 3. #10590807 | C2 | semidirect |
| 4. C2×#63548 | C2 | semidirect |
| 5. C3×#4509 | C2 | semidirect |
| 6. C3×Dic3⋊C16 | C2 | semidirect |
| 7. #10589116 | C2 | semidirect |
| 35. #4509 | D3 | semidirect |
| 36. Dic3⋊C16 | D3 | semidirect |
| 45. #3746 | D4 | semidirect |
| 174. C3×Dic3 | SD32 | semidirect |
| 290. Dic3 | #800 | semidirect |
| 291. C32 | #2207 | semidirect |
| 338. C3 | #69204 | semidirect |
| 339. C3 | #69292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63627 | 2 |
| #10590880 | 2 |
| #10590807 | 2 |
| C2×#63548 | 2 |
| C3×#4509 | 2 |
| C3×Dic3⋊C16 | 2 |
| #10589116 | 2 |
| #69292 | 3 |
| #69204 | 3 |