Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
336 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 77 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×C4⋊(C3⋊D9) | C2 | semidirect |
| 2. C2×C4×D3×C9 | C2 | semidirect |
| 3. C2×#6195 | C2 | semidirect |
| 4. C3×C4⋊Dic9 | C2 | semidirect |
| 5. #88445 | C2 | semidirect |
| 26. C4⋊Dic9 | D3 | semidirect |
| 33. C2×D3×C9 | D4 | semidirect |
| 34. C3×C4×C9 | D4 | semidirect |
| 69. C2×C4×D3 | D9 | semidirect |
| 97. C4×C9 | D12 | semidirect |
| 100. C3×C9 | #121 | semidirect |
| 156. C2×D3 | D36 | semidirect |
| 160. C3×C4 | #611 | semidirect |
| 166. C9 | #895 | semidirect |
| 198. C4 | #6195 | semidirect |
| 200. C3 | #63492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊D9) | 2 |
| C2×C4×D3×C9 | 2 |
| C2×#6195 | 2 |
| C3×C4⋊Dic9 | 2 |
| #88445 | 2 |
| #63909 | 3 |
| #63492 | 3 |