Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
266 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 61 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. C9×(C2×D3)⋊C4 | C2 | semidirect |
| 4. C3×(C2×D9)⋊C4 | C2 | semidirect |
| 5. (C2×D3)⋊Dic9 | C2 | semidirect |
| 6. (C2×D9)⋊Dic3 | C2 | semidirect |
| 7. Dic3×Dic9 | C2 | semidirect |
| 32. (C2×D9)⋊C4 | D3 | semidirect |
| 87. (C2×D3)⋊C4 | D9 | semidirect |
| 119. C3×C9 | #124 | semidirect |
| 192. C9 | #885 | semidirect |
| 228. C3 | #63447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6226 | 2 |
| C2×#6194 | 2 |
| C9×(C2×D3)⋊C4 | 2 |
| C3×(C2×D9)⋊C4 | 2 |
| (C2×D3)⋊Dic9 | 2 |
| (C2×D9)⋊Dic3 | 2 |
| Dic3×Dic9 | 2 |
| #63913 | 3 |
| #63447 | 3 |