Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
307 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 307 conjugacy classes of subgroups — too many to draw. Only its 98 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×#4874 | C2 | semidirect |
| 3. C32×#366 | C2 | semidirect |
| 5. C3×Dic3⋊C16 | C2 | semidirect |
| 7. C3×#4489 | C2 | semidirect |
| 9. #69333 | C3 | direct (N × H) |
| 23. #4874 | C2×C3 | semidirect |
| 27. C3×#366 | D3 | semidirect |
| 28. C3×#366 | C2×C3 | semidirect |
| 33. Dic3⋊C16 | C2×C3 | semidirect |
| 35. #4489 | C2×C3 | semidirect |
| 48. C3×D24 | Q8 | semidirect |
| 94. #366 | C3×D3 | semidirect |
| 126. D24 | C3×Q8 | semidirect |
| 233. C32 | #2224 | semidirect |
| 271. C3 | #69333 | direct (N × H) |
| 272. C3 | C3×#2224 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4874 | 2 |
| C3×#4872 | 2 |
| C32×#366 | 2 |
| C3×#4509 | 2 |
| C3×Dic3⋊C16 | 2 |
| C3×#4491 | 2 |
| C3×#4489 | 2 |
| C3×#2224 | 3 |
| #69333 | 3 |