Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
288 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×C3×C4×C9 | C2 | semidirect |
| 3. C9×#217 | C2 | semidirect |
| 4. C9×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C9×Dic3⋊C4 | C2 | semidirect |
| 22. C22×C4×C9 | D3 | semidirect |
| 35. #929 | C9 | direct (N × H) |
| 59. C22×C3×C4 | C2×C9 | semidirect |
| 65. #217 | C2×C9 | semidirect |
| 66. (C2×D3)⋊C4 | C2×C9 | semidirect |
| 67. Dic3⋊C4 | C2×C9 | semidirect |
| 89. C3×C9 | #123 | semidirect |
| 119. C22×C4 | D3×C9 | semidirect |
| 145. C9 | #929 | direct (N × H) |
| 173. C3 | C9×#123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×C9 | 2 |
| C2×C9×#67 | 2 |
| C9×#217 | 2 |
| C9×(C2×D3)⋊C4 | 2 |
| C9×Dic3⋊C4 | 2 |
| C3×#929 | 3 |
| C9×#123 | 3 |