Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
285 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 285 conjugacy classes of subgroups — too many to draw. Only its 85 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. C9×#117 | C2 | semidirect |
| 3. C2×#3667 | C2 | semidirect |
| 4. #63369 | C2 | semidirect |
| 10. C2×D36 | C4 | semidirect |
| 12. C9×C4⋊C4 | C22 | semidirect |
| 16. C2×C9⋊C8 | C22 | semidirect |
| 58. #117 | D9 | semidirect |
| 85. C4⋊C4 | C2×D9 | semidirect |
| 98. C9 | #418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D36 | 2 |
| C9×#117 | 2 |
| C2×#3667 | 2 |
| #63369 | 2 |
| #5001 | 3 |