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. #10590891 | C2 | semidirect |
| 4. C3×#4504 | C2 | semidirect |
| 5. C3×Dic3⋊C16 | C2 | semidirect |
| 6. #10589139 | C2 | semidirect |
| 32. #4504 | D3 | semidirect |
| 33. Dic3⋊C16 | D3 | semidirect |
| 42. #3745 | Q8 | semidirect |
| 239. C32 | #2224 | semidirect |
| 278. C3 | #69289 | semidirect |
| 279. C3 | #69333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590891 | 2 |
| #10590763 | 2 |
| #10589375 | 2 |
| C3×#4504 | 2 |
| C3×Dic3⋊C16 | 2 |
| #10589139 | 2 |
| #10589116 | 2 |
| #69333 | 3 |
| #69289 | 3 |