Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
300 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 95 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. #64078 | C2 | semidirect |
| 3. C32×#97 | C2 | semidirect |
| 5. #63643 | C2 | semidirect |
| 18. C3×#97 | D3 | semidirect |
| 54. #97 | C3⋊D3 | semidirect |
| 87. C32 | #489 | semidirect |
| 111. C3 | #4714 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64084 | 2 |
| #64078 | 2 |
| C32×#97 | 2 |
| #63648 | 2 |
| #63643 | 2 |
| #4714 | 3 |