Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
331 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 331 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. C3×#4717 | C2 | semidirect |
| 2. C3×#4711 | C2 | semidirect |
| 4. #10589332 | C2 | semidirect |
| 5. #10589138 | C2 | semidirect |
| 6. #10589126 | C2 | semidirect |
| 7. #10589123 | C2 | semidirect |
| 21. #63547 | C4 | semidirect |
| 22. #63545 | C4 | semidirect |
| 27. #4717 | D3 | semidirect |
| 28. #4711 | D3 | semidirect |
| 47. C3×Dic12 | C2×C4 | semidirect |
| 50. C3×D24 | C2×C4 | semidirect |
| 55. C3⋊(C3⋊C16) | C2×C4 | semidirect |
| 136. Dic12 | C4×D3 | semidirect |
| 139. D24 | C4×D3 | semidirect |
| 253. C32 | AGL(1,ℤ/16) | semidirect |
| 290. C3 | #70918 | semidirect |
| 291. C3 | #70929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4717 | 2 |
| C3×#4711 | 2 |
| #10590630 | 2 |
| #10589332 | 2 |
| #10589138 | 2 |
| #10589126 | 2 |
| #10589123 | 2 |
| #70929 | 3 |
| #70918 | 3 |