Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
183 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 183 conjugacy classes of subgroups — too many to draw. Only its 73 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. #63367 | C2 | semidirect |
| 7. C4×C9⋊C8 | C2 | semidirect |
| 16. #3675 | C4 | direct (N × H) |
| 30. Q8×C9 | C2×C4 | semidirect |
| 41. C9⋊C8 | C2×C4 | semidirect |
| 62. C4×C9 | SD16 | semidirect |
| 67. C4×Q8 | D9 | semidirect |
| 114. C9 | C4×SD16 | semidirect |
| 117. Q8 | C4×D9 | semidirect |
| 141. C4 | #3675 | direct (N × H) |
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 |
| #63367 | 2 |
| C4×C9⋊C8 | 2 |
| C4×#215 | 3 |