Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
224 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 70 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×D3×Q32 | C2 | semidirect |
| 3. C32×SD64 | C2 | semidirect |
| 4. C3×#4522 | C2 | semidirect |
| 5. C3×#4520 | C2 | semidirect |
| 6. C3×Dic48 | C2 | semidirect |
| 7. C3×#4447 | C2 | semidirect |
| 9. #69381 | C3 | direct (N × H) |
| 23. D3×Q32 | C2×C3 | semidirect |
| 29. C3×SD64 | D3 | semidirect |
| 30. C3×SD64 | C2×C3 | semidirect |
| 32. #4522 | C2×C3 | semidirect |
| 33. #4520 | C2×C3 | semidirect |
| 34. Dic48 | C2×C3 | semidirect |
| 35. #4447 | C2×C3 | semidirect |
| 89. SD64 | C3×D3 | semidirect |
| 190. C32 | #2264 | semidirect |
| 218. C3 | #69381 | direct (N × H) |
| 219. C3 | C3×#2264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D3×Q32 | 2 |
| C3×#4912 | 2 |
| C32×SD64 | 2 |
| C3×#4522 | 2 |
| C3×#4520 | 2 |
| C3×Dic48 | 2 |
| C3×#4447 | 2 |
| C3×#2264 | 3 |
| #69381 | 3 |