Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
283 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 283 conjugacy classes of subgroups — too many to draw. Only its 94 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. C32×#499 | C2 | semidirect |
| 4. C3×#4487 | C2 | semidirect |
| 5. C3×#4463 | C2 | semidirect |
| 7. #71358 | C3 | direct (N × H) |
| 18. C3×#499 | D3 | semidirect |
| 19. C3×#499 | C2×C3 | semidirect |
| 26. #4487 | C2×C3 | semidirect |
| 27. #4463 | C2×C3 | semidirect |
| 76. #499 | C3×D3 | semidirect |
| 194. C32 | #2231 | semidirect |
| 223. C3 | #71358 | direct (N × H) |
| 224. C3 | C3×#2231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#499 | 2 |
| C3×#4700 | 2 |
| C3×#4488 | 2 |
| C3×#4487 | 2 |
| C3×#4463 | 2 |
| C3×#2231 | 3 |
| #71358 | 3 |