Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
385 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 385 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. C2×C32×SD32 | C2 | semidirect |
| 2. C3×#5191 | C2 | semidirect |
| 3. C3×Dic3×D8 | C2 | semidirect |
| 5. C3×#4564 | C2 | semidirect |
| 6. C3×#4509 | C2 | semidirect |
| 7. C3×Dic3⋊C16 | C2 | semidirect |
| 9. #71477 | C3 | direct (N × H) |
| 24. C2×C3×SD32 | D3 | semidirect |
| 25. C2×C3×SD32 | C2×C3 | semidirect |
| 29. #5191 | C2×C3 | semidirect |
| 30. Dic3×D8 | C2×C3 | semidirect |
| 35. #4564 | C2×C3 | semidirect |
| 36. #4509 | C2×C3 | semidirect |
| 37. Dic3⋊C16 | C2×C3 | semidirect |
| 106. C2×SD32 | C3×D3 | semidirect |
| 288. C32 | #2210 | semidirect |
| 334. C3 | #71477 | direct (N × H) |
| 335. C3 | C3×#2210 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×SD32 | 2 |
| C3×#5191 | 2 |
| C3×Dic3×D8 | 2 |
| C2×C3×#826 | 2 |
| C3×#4564 | 2 |
| C3×#4509 | 2 |
| C3×Dic3⋊C16 | 2 |
| C3×#2210 | 3 |
| #71477 | 3 |