Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
353 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 353 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 2. C3×#4874 | C2 | semidirect |
| 3. C32×#357 | C2 | semidirect |
| 4. C3×#4562 | C2 | semidirect |
| 5. C3×#4509 | C2 | semidirect |
| 6. C3×Dic3×C16 | C2 | semidirect |
| 7. C3×#4491 | C2 | semidirect |
| 9. #69183 | C3 | direct (N × H) |
| 24. #4874 | C2×C3 | semidirect |
| 29. C3×#357 | D3 | semidirect |
| 30. C3×#357 | C2×C3 | semidirect |
| 32. #4562 | C2×C3 | semidirect |
| 33. #4509 | C2×C3 | semidirect |
| 34. Dic3×C16 | C2×C3 | semidirect |
| 35. #4491 | C2×C3 | semidirect |
| 102. #357 | C3×D3 | semidirect |
| 267. C32 | #2240 | semidirect |
| 313. C3 | #69183 | direct (N × H) |
| 314. C3 | C3×#2240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5151 | 2 |
| C3×#4874 | 2 |
| C32×#357 | 2 |
| C3×#4562 | 2 |
| C3×#4509 | 2 |
| C3×Dic3×C16 | 2 |
| C3×#4491 | 2 |
| C3×#2240 | 3 |
| #69183 | 3 |