Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
199 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 199 conjugacy classes of subgroups — too many to draw. Only its 56 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. #64113 | C2 | semidirect |
| 2. C3×#904 | C2 | semidirect |
| 3. C2×C3×C3⋊C16 | C2 | semidirect |
| 4. #63551 | C2 | semidirect |
| 5. #63549 | C2 | semidirect |
| 6. #63548 | C2 | semidirect |
| 7. #63546 | C2 | semidirect |
| 25. #904 | D3 | semidirect |
| 31. C2×C3⋊C16 | D3 | semidirect |
| 152. C32 | #508 | semidirect |
| 183. C3 | #4904 | semidirect |
| 184. C3 | #5194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64113 | 2 |
| C3×#904 | 2 |
| C2×C3×C3⋊C16 | 2 |
| #63551 | 2 |
| #63549 | 2 |
| #63548 | 2 |
| #63546 | 2 |
| #5194 | 3 |
| #4904 | 3 |