Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
316 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 316 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×C4×D3×C9 | C2 | semidirect |
| 2. C2×#6195 | C2 | semidirect |
| 3. C2×#6194 | C2 | semidirect |
| 4. C2×#6192 | C2 | semidirect |
| 5. #88536 | C2 | semidirect |
| 6. C3×(C2×D9)⋊C4 | C2 | semidirect |
| 7. Dic3⋊Dic9 | C2 | semidirect |
| 34. (C2×D9)⋊C4 | D3 | semidirect |
| 42. C2×D3×C9 | D4 | semidirect |
| 48. C9×Dic3 | D4 | semidirect |
| 90. C2×C4×D3 | D9 | semidirect |
| 133. C3×C9 | #121 | semidirect |
| 205. C2×D3 | D36 | semidirect |
| 215. Dic3 | #611 | semidirect |
| 218. C9 | #884 | semidirect |
| 261. C3 | #63492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D3×C9 | 2 |
| C2×#6195 | 2 |
| C2×#6194 | 2 |
| C2×#6192 | 2 |
| #88536 | 2 |
| C3×(C2×D9)⋊C4 | 2 |
| Dic3⋊Dic9 | 2 |
| #63906 | 3 |
| #63492 | 3 |