Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
274 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 60 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. C2×#3743 | C2 | semidirect |
| 3. #63871 | C2 | semidirect |
| 4. C2×#3715 | C2 | semidirect |
| 5. C3×#821 | C2 | semidirect |
| 6. C3×#816 | C2 | semidirect |
| 7. #63576 | C2 | semidirect |
| 34. #821 | D3 | semidirect |
| 35. #816 | D3 | semidirect |
| 53. C3⋊(C3⋊C8) | D4 | semidirect |
| 195. C32 | #468 | semidirect |
| 240. C3 | #4780 | semidirect |
| 241. C3 | #4812 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3743 | 2 |
| #63916 | 2 |
| #63871 | 2 |
| C2×#3715 | 2 |
| C3×#821 | 2 |
| C3×#816 | 2 |
| #63576 | 2 |
| #4812 | 3 |
| #4780 | 3 |