Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
317 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 317 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. C3×#4874 | C2 | semidirect |
| 4. C3×#4489 | C2 | semidirect |
| 5. #10589140 | C2 | semidirect |
| 6. Dic3⋊(C3⋊C16) | C2 | semidirect |
| 22. #4874 | D3 | semidirect |
| 34. #4489 | D3 | semidirect |
| 42. #3745 | Q8 | semidirect |
| 239. C32 | #2224 | semidirect |
| 278. C3 | #69333 | semidirect |
| 279. C3 | #71387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4874 | 2 |
| #10590763 | 2 |
| #10589357 | 2 |
| C3×#4489 | 2 |
| #10589140 | 2 |
| Dic3⋊(C3⋊C16) | 2 |
| #10589116 | 2 |
| #71387 | 3 |
| #69333 | 3 |