Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
288 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #64099 | C2 | semidirect |
| 5. #63643 | C2 | semidirect |
| 6. C8×C3⋊Dic3 | C2 | semidirect |
| 7. #63637 | C2 | semidirect |
| 109. C32 | #488 | semidirect |
| 138. C3 | #4768 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64145 | 2 |
| #64099 | 2 |
| C32×#102 | 2 |
| #63659 | 2 |
| #63643 | 2 |
| C8×C3⋊Dic3 | 2 |
| #63637 | 2 |
| #4768 | 3 |