Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
150 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 53 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. #63431 | C2 | semidirect |
| 3. #63395 | C2 | semidirect |
| 5. #63362 | C2 | semidirect |
| 87. C9 | #489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#124 | 2 |
| #63431 | 2 |
| #63395 | 2 |
| #63392 | 2 |
| #63362 | 2 |
| #5055 | 3 |