Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
334 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 4. C3×#816 | C2 | semidirect |
| 5. #63565 | C2 | semidirect |
| 12. #3797 | C4 | semidirect |
| 25. #816 | D3 | semidirect |
| 128. C32 | #419 | semidirect |
| 158. C3 | #4802 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3797 | 2 |
| C2×#3743 | 2 |
| #63849 | 2 |
| C3×#816 | 2 |
| #63565 | 2 |
| #4802 | 3 |