Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
289 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 289 conjugacy classes of subgroups — too many to draw. Only its 74 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×#893 | C2 | semidirect |
| 2. #63894 | C2 | semidirect |
| 4. #63636 | C2 | semidirect |
| 5. C3×#808 | C2 | semidirect |
| 6. #63562 | C2 | semidirect |
| 7. #63554 | C2 | semidirect |
| 21. #3714 | C4 | semidirect |
| 26. #893 | D3 | semidirect |
| 35. #808 | D3 | semidirect |
| 42. C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 47. C3×D12 | C2×C4 | semidirect |
| 51. C3×C3⋊C8 | C2×C4 | semidirect |
| 127. D12 | C4×D3 | semidirect |
| 135. C3⋊C8 | C4×D3 | semidirect |
| 186. C32 | #442 | semidirect |
| 230. C3 | #4869 | semidirect |
| 231. C3 | #5014 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#893 | 2 |
| #63894 | 2 |
| C2×#3714 | 2 |
| #63636 | 2 |
| C3×#808 | 2 |
| #63562 | 2 |
| #63554 | 2 |
| #5014 | 3 |
| #4869 | 3 |