Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
395 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 395 conjugacy classes of subgroups — too many to draw. Only its 110 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×#4848 | C2 | semidirect |
| 3. C3×#4679 | C2 | semidirect |
| 4. C32×#334 | C2 | semidirect |
| 5. C3×#4485 | C2 | semidirect |
| 7. #68550 | C3 | direct (N × H) |
| 22. #4848 | C2×C3 | semidirect |
| 24. #4679 | C2×C3 | semidirect |
| 26. C3×#334 | D3 | semidirect |
| 27. C3×#334 | C2×C3 | semidirect |
| 29. #4485 | C2×C3 | semidirect |
| 84. C32×C8 | SD16 | semidirect |
| 89. #334 | C3×D3 | semidirect |
| 181. C3×C8 | #204 | semidirect |
| 182. C3×C8 | C3×SD16 | semidirect |
| 228. C32 | #1688 | semidirect |
| 244. C8 | C3×#204 | semidirect |
| 267. C3 | #68550 | direct (N × H) |
| 268. C3 | C3×#1688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4848 | 2 |
| C3×#4695 | 2 |
| C3×#4679 | 2 |
| C32×#334 | 2 |
| C3×#4485 | 2 |
| C3×#1688 | 3 |
| #68550 | 3 |