Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
266 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×#6226 | C2 | semidirect |
| 3. C3×C4×Dic9 | C2 | semidirect |
| 4. (C2×D3)⋊Dic9 | C2 | semidirect |
| 21. C4×Dic9 | D3 | semidirect |
| 73. C3×C9 | #124 | semidirect |
| 118. C9 | #875 | semidirect |
| 140. C3 | #63498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6226 | 2 |
| C2×C9×D12 | 2 |
| C3×C4×Dic9 | 2 |
| (C2×D3)⋊Dic9 | 2 |
| #63860 | 3 |
| #63498 | 3 |