Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
180 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 67 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. C4×Q8×C9 | C2 | semidirect |
| 4. #63395 | C2 | semidirect |
| 6. #63366 | C2 | semidirect |
| 7. #63362 | C2 | semidirect |
| 16. #3675 | C4 | semidirect |
| 30. Q8×C9 | C2×C4 | semidirect |
| 41. C9⋊C8 | C2×C4 | semidirect |
| 67. C4×Q8 | D9 | semidirect |
| 114. C9 | #440 | semidirect |
| 117. Q8 | C4×D9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×C9 | 2 |
| C2×#3675 | 2 |
| C4×D36 | 2 |
| #63395 | 2 |
| #63369 | 2 |
| #63366 | 2 |
| #63362 | 2 |
| #5026 | 3 |