Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
201 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 201 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 1. C9×#121 | C2 | semidirect |
| 2. C2×#3673 | C2 | semidirect |
| 3. #63492 | C2 | semidirect |
| 4. C22×C9⋊C8 | C2 | semidirect |
| 5. #63392 | C2 | semidirect |
| 6. #63369 | C2 | semidirect |
| 7. #63366 | C2 | semidirect |
| 45. C9⋊C8 | D4 | semidirect |
| 65. C22×C9 | D8 | semidirect |
| 78. #121 | D9 | semidirect |
| 133. C9 | #466 | semidirect |
| 165. C22 | #3673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#121 | 2 |
| C2×#3673 | 2 |
| #63492 | 2 |
| C22×C9⋊C8 | 2 |
| #63392 | 2 |
| #63369 | 2 |
| #63366 | 2 |
| #5038 | 3 |