Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
357 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 357 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
| 4. C3×#4546 | C2 | semidirect |
| 5. C3×#4457 | C2 | semidirect |
| 7. #71374 | C3 | direct (N × H) |
| 20. C3×#500 | D3 | semidirect |
| 21. C3×#500 | C2×C3 | semidirect |
| 28. #4546 | C2×C3 | semidirect |
| 29. #4457 | C2×C3 | semidirect |
| 84. #500 | C3×D3 | semidirect |
| 220. C32 | #1695 | semidirect |
| 257. C3 | #71374 | direct (N × H) |
| 258. C3 | C3×#1695 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#500 | 2 |
| C3×#5084 | 2 |
| C3×#4688 | 2 |
| C3×#4546 | 2 |
| C3×#4457 | 2 |
| C3×#1695 | 3 |
| #71374 | 3 |