Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
273 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 273 conjugacy classes of subgroups — too many to draw. Only its 82 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×D16 | C2 | semidirect |
| 2. C3×#4904 | C2 | semidirect |
| 3. C3×#4520 | C2 | semidirect |
| 4. C3×#4519 | C2 | semidirect |
| 5. C3×#4499 | C2 | semidirect |
| 7. #71458 | C3 | direct (N × H) |
| 13. C3×Dic24 | C22 | semidirect |
| 15. C3×D48 | C22 | semidirect |
| 16. C3×C3⋊C32 | C22 | semidirect |
| 19. C2×C3×D16 | D3 | semidirect |
| 20. C2×C3×D16 | C2×C3 | semidirect |
| 21. #4904 | C2×C3 | semidirect |
| 25. #4520 | C2×C3 | semidirect |
| 26. #4519 | C2×C3 | semidirect |
| 27. #4499 | C2×C3 | semidirect |
| 56. Dic24 | C22×C3 | semidirect |
| 58. D48 | C22×C3 | semidirect |
| 60. C3⋊C32 | C22×C3 | semidirect |
| 72. C2×D16 | C3×D3 | semidirect |
| 177. C32 | #2263 | semidirect |
| 207. C3 | #71458 | direct (N × H) |
| 208. C3 | C3×#2263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D16 | 2 |
| C3×#4904 | 2 |
| C3×#4520 | 2 |
| C3×#4519 | 2 |
| C3×#4499 | 2 |
| C3×#2263 | 3 |
| #71458 | 3 |