Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
288 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 103 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. #63642 | C2 | semidirect |
| 5. #63641 | C2 | semidirect |
| 6. #63641 | C2 | semidirect |
| 7. C8×C3⋊Dic3 | C2 | semidirect |
| 109. C32 | #433 | semidirect |
| 138. C3 | #4720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64135 | 2 |
| C32×C22⋊C8 | 2 |
| #63657 | 2 |
| #63642 | 2 |
| #63641 | 2 |
| C8×C3⋊Dic3 | 2 |
| #4720 | 3 |