Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
390 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 1. Q8×C22⋊C9 | C2 | semidirect |
| 2. D4×C22⋊C9 | C2 | semidirect |
| 3. C2×C4×C22⋊C9 | C2 | semidirect |
| 21. C22×#41 | C9 | semidirect |
| 42. C22⋊C9 | #41 | direct (N × H) |
| 49. C22×Q8 | C2×C9 | semidirect |
| 50. C22×D4 | C2×C9 | semidirect |
| 51. C23×C4 | C2×C9 | semidirect |
| 82. #41 | C22⋊C9 | direct (N × H) |
| 115. Q8 | C2×C22⋊C9 | semidirect |
| 119. D4 | C2×C22⋊C9 | semidirect |
| 128. C2×C4 | C2×C22⋊C9 | semidirect |
| 141. C22 | C9×#41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C22⋊C9 | 2 |
| D4×C22⋊C9 | 2 |
| C2×C4×C22⋊C9 | 2 |
| C22×C3×#41 | 3 |
| C9×#41 | 4 |