Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
192 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. C9×#208 | C2 | semidirect |
| 19. #833 | C9 | direct (N × H) |
| 38. #208 | C2×C9 | semidirect |
| 52. C3×C9 | #100 | semidirect |
| 89. C9 | #833 | direct (N × H) |
| 108. C3 | C9×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×C9 | 2 |
| C9×#208 | 2 |
| C3×#833 | 3 |
| C9×#100 | 3 |