Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
489 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 489 conjugacy classes of subgroups — too many to draw. Only its 130 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×#498 | C2 | semidirect |
| 2. C3×#5088 | C2 | semidirect |
| 3. C3×#5085 | C2 | semidirect |
| 5. C3×#4455 | C2 | semidirect |
| 7. #71336 | C3 | direct (N × H) |
| 18. C3×#498 | D3 | semidirect |
| 19. C3×#498 | C2×C3 | semidirect |
| 23. #5088 | C2×C3 | semidirect |
| 24. #5085 | C2×C3 | semidirect |
| 27. #4455 | C2×C3 | semidirect |
| 72. C32×C8 | SD16 | semidirect |
| 74. #498 | C3×D3 | semidirect |
| 151. C3×C8 | #215 | semidirect |
| 152. C3×C8 | C3×SD16 | semidirect |
| 190. C32 | #1715 | semidirect |
| 202. C8 | C3×#215 | semidirect |
| 222. C3 | #71336 | direct (N × H) |
| 223. C3 | C3×#1715 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#498 | 2 |
| C3×#5088 | 2 |
| C3×#5085 | 2 |
| C3×#4695 | 2 |
| C3×#4455 | 2 |
| C3×#1715 | 3 |
| #71336 | 3 |