Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
438 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 438 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. #63651 | C2 | direct (N × H) |
| 86. C2×C32 | #101 | semidirect |
| 111. C32 | C2×#101 | semidirect |
| 130. C2×C3 | #824 | semidirect |
| 141. C3 | C2×#824 | semidirect |
| 144. C2 | #63651 | direct (N × H) |
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 |
| C2×#3748 | 2 |
| #63651 | 2 |
| C2×#824 | 3 |