Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
365 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 365 conjugacy classes of subgroups — too many to draw. Only its 106 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×C32×#107 | C2 | semidirect |
| 3. C3×#4549 | C2 | semidirect |
| 4. C3×#4491 | C2 | semidirect |
| 5. C3×#4489 | C2 | semidirect |
| 7. #70599 | C3 | direct (N × H) |
| 19. C2×C3×#107 | D3 | semidirect |
| 20. C2×C3×#107 | C2×C3 | semidirect |
| 25. #4549 | C2×C3 | semidirect |
| 26. #4491 | C2×C3 | semidirect |
| 27. #4489 | C2×C3 | semidirect |
| 79. C2×#107 | C3×D3 | semidirect |
| 224. C32 | #2232 | semidirect |
| 266. C3 | #70599 | direct (N × H) |
| 267. C3 | C3×#2232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#107 | 2 |
| C3×#5115 | 2 |
| C3×#4549 | 2 |
| C3×#4491 | 2 |
| C3×#4489 | 2 |
| C3×#2232 | 3 |
| #70599 | 3 |