Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
393 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 393 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×#494 | C2 | semidirect |
| 4. C3×#4547 | C2 | semidirect |
| 5. C3×#4457 | C2 | semidirect |
| 7. #71306 | C3 | direct (N × H) |
| 20. C3×#494 | D3 | semidirect |
| 21. C3×#494 | C2×C3 | semidirect |
| 28. #4547 | C2×C3 | semidirect |
| 29. #4457 | C2×C3 | semidirect |
| 87. #494 | C3×D3 | semidirect |
| 234. C32 | #1689 | semidirect |
| 272. C3 | #71306 | direct (N × H) |
| 273. C3 | C3×#1689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#494 | 2 |
| C3×#5087 | 2 |
| C3×#4688 | 2 |
| C3×#4547 | 2 |
| C3×#4457 | 2 |
| C3×#1689 | 3 |
| #71306 | 3 |