Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
336 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 65 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×#6195 | C2 | semidirect |
| 3. C2×#6195 | C2 | semidirect |
| 4. C2×(C3⋊D9)⋊C4 | C2 | semidirect |
| 5. C9×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C3×Dic9⋊C4 | C2 | semidirect |
| 7. #88445 | C2 | semidirect |
| 35. Dic9⋊C4 | D3 | semidirect |
| 42. C2×C3⋊D9 | D4 | semidirect |
| 49. C3×Dic9 | D4 | semidirect |
| 97. (C2×D3)⋊C4 | D9 | semidirect |
| 134. Dic9 | D12 | semidirect |
| 136. C3×C9 | #121 | semidirect |
| 225. C9 | #895 | semidirect |
| 269. C3 | #63446 | 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×#6195 | 2 |
| C2×(C3⋊D9)⋊C4 | 2 |
| C9×(C2×D3)⋊C4 | 2 |
| C3×Dic9⋊C4 | 2 |
| #88445 | 2 |
| #63910 | 3 |
| #63446 | 3 |