Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
421 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 421 conjugacy classes of subgroups — too many to draw. Only its 114 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. C32×#500 | C2 | semidirect |
| 2. C3×#5093 | C2 | semidirect |
| 5. C3×#5079 | C2 | semidirect |
| 7. C3×#4454 | C2 | semidirect |
| 9. #71365 | C3 | direct (N × H) |
| 24. C3×#500 | D3 | semidirect |
| 25. C3×#500 | C2×C3 | semidirect |
| 31. #5093 | C2×C3 | semidirect |
| 34. #5079 | C2×C3 | semidirect |
| 37. #4454 | C2×C3 | semidirect |
| 102. #500 | C3×D3 | semidirect |
| 261. C32 | #1719 | semidirect |
| 300. C3 | #71365 | direct (N × H) |
| 301. C3 | C3×#1719 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#500 | 2 |
| C3×#5093 | 2 |
| C3×#5088 | 2 |
| C3×#5085 | 2 |
| C3×#5079 | 2 |
| C3×#4694 | 2 |
| C3×#4454 | 2 |
| C3×#1719 | 3 |
| #71365 | 3 |