Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
367 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 367 conjugacy classes of subgroups — too many to draw. Only its 90 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×#4872 | C2 | semidirect |
| 2. Dic3×D24 | C2 | semidirect |
| 4. #10589356 | C2 | semidirect |
| 5. C3×#4491 | C2 | semidirect |
| 6. #10589115 | C2 | semidirect |
| 7. #10589103 | C2 | semidirect |
| 21. #63545 | C4 | semidirect |
| 26. #4872 | D3 | semidirect |
| 32. #4491 | D3 | semidirect |
| 49. C3×D24 | C2×C4 | semidirect |
| 50. C3×D24 | C2×C4 | semidirect |
| 52. C3⋊(C3⋊C16) | C2×C4 | semidirect |
| 136. D24 | C4×D3 | semidirect |
| 137. D24 | C4×D3 | semidirect |
| 258. C32 | #2177 | semidirect |
| 302. C3 | #69177 | semidirect |
| 303. C3 | #70885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4872 | 2 |
| Dic3×D24 | 2 |
| C2×#63545 | 2 |
| #10589356 | 2 |
| C3×#4491 | 2 |
| #10589115 | 2 |
| #10589103 | 2 |
| #70885 | 3 |
| #69177 | 3 |