Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
450 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 151 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. #63643 | C2 | semidirect |
| 10. C2×#634 | C4 | semidirect |
| 91. C32 | #419 | semidirect |
| 115. C3 | #5120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#634 | 2 |
| C2×C32×M16 | 2 |
| #64135 | 2 |
| #63643 | 2 |
| #5120 | 3 |