Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
361 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 361 conjugacy classes of subgroups — too many to draw. Only its 84 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×#5183 | C2 | semidirect |
| 5. #10589430 | C2 | semidirect |
| 6. Dic3⋊(C3⋊C16) | C2 | semidirect |
| 7. #10589118 | C2 | semidirect |
| 25. #5183 | D3 | semidirect |
| 168. C3×Dic3 | SD32 | semidirect |
| 273. Dic3 | #828 | semidirect |
| 274. C32 | #2208 | semidirect |
| 315. C3 | #71315 | semidirect |
| 316. C3 | #71476 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5183 | 2 |
| C2×C3×#828 | 2 |
| Dic3×D24 | 2 |
| C2×#63547 | 2 |
| #10589430 | 2 |
| Dic3⋊(C3⋊C16) | 2 |
| #10589118 | 2 |
| #71476 | 3 |
| #71315 | 3 |