Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
315 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 315 conjugacy classes of subgroups — too many to draw. Only its 76 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. #64139 | C2 | semidirect |
| 2. C3×#930 | C2 | semidirect |
| 3. C22×C3×C3⋊C8 | C2 | semidirect |
| 4. C2×#3714 | C2 | semidirect |
| 5. #63575 | C2 | semidirect |
| 6. #63564 | C2 | semidirect |
| 7. #63563 | C2 | semidirect |
| 29. #930 | D3 | semidirect |
| 30. C22×C3⋊C8 | D3 | semidirect |
| 54. C3×C3⋊C8 | D4 | semidirect |
| 89. C22×C32 | D8 | semidirect |
| 152. C3⋊C8 | #67 | semidirect |
| 183. C22×C3 | D24 | semidirect |
| 184. C22×C3 | #213 | semidirect |
| 213. C32 | #466 | semidirect |
| 256. C22 | #3714 | semidirect |
| 264. C3 | #5038 | semidirect |
| 265. C3 | #5115 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64139 | 2 |
| C3×#930 | 2 |
| C22×C3×C3⋊C8 | 2 |
| C2×#3714 | 2 |
| #63575 | 2 |
| #63564 | 2 |
| #63563 | 2 |
| #5115 | 3 |
| #5038 | 3 |