Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
305 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 305 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 |
|---|---|---|
| 2. C3×#4878 | C2 | semidirect |
| 5. C3×#4504 | C2 | semidirect |
| 6. C3×Dic3⋊C16 | C2 | semidirect |
| 7. C3×#4490 | C2 | semidirect |
| 9. #69180 | C3 | direct (N × H) |
| 24. #4878 | C2×C3 | semidirect |
| 33. #4504 | C2×C3 | semidirect |
| 34. Dic3⋊C16 | C2×C3 | semidirect |
| 35. #4490 | C2×C3 | semidirect |
| 236. C32 | #2228 | semidirect |
| 274. C3 | #69180 | direct (N × H) |
| 275. C3 | C3×#2228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Dic3×D8 | 2 |
| C3×#4878 | 2 |
| C32×#357 | 2 |
| C3×#4562 | 2 |
| C3×#4504 | 2 |
| C3×Dic3⋊C16 | 2 |
| C3×#4490 | 2 |
| C3×#2228 | 3 |
| #69180 | 3 |