Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
306 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 139 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. #63649 | C2 | semidirect |
| 85. C32 | #430 | semidirect |
| 108. C3 | #5124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×M16 | 2 |
| C2×#3748 | 2 |
| #63649 | 2 |
| #5124 | 3 |