Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
377 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 377 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×#5183 | C2 | semidirect |
| 5. C3×#4564 | C2 | semidirect |
| 6. C3×#4503 | C2 | semidirect |
| 7. C3×Dic3⋊C16 | C2 | semidirect |
| 9. #71476 | C3 | direct (N × H) |
| 29. #5183 | C2×C3 | semidirect |
| 35. #4564 | C2×C3 | semidirect |
| 36. #4503 | C2×C3 | semidirect |
| 37. Dic3⋊C16 | C2×C3 | semidirect |
| 171. C3×Dic3 | SD32 | semidirect |
| 280. Dic3 | C3×SD32 | semidirect |
| 281. C32 | #2208 | semidirect |
| 323. C3 | #71476 | direct (N × H) |
| 324. C3 | C3×#2208 | 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×#5183 | 2 |
| C3×Dic3×D8 | 2 |
| C2×C3×#827 | 2 |
| C3×#4564 | 2 |
| C3×#4503 | 2 |
| C3×Dic3⋊C16 | 2 |
| C3×#2208 | 3 |
| #71476 | 3 |