Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
316 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 79 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×C3×C4×D9 | C2 | semidirect |
| 3. C2×(C3⋊D9)⋊C4 | C2 | semidirect |
| 4. #88536 | C2 | semidirect |
| 5. C9×Dic3⋊C4 | C2 | semidirect |
| 6. (C2×D9)⋊Dic3 | C2 | semidirect |
| 7. Dic3×Dic9 | C2 | semidirect |
| 18. #6192 | C4 | semidirect |
| 29. C2×C4×D9 | D3 | semidirect |
| 38. C2×C3⋊D9 | C2×C4 | semidirect |
| 41. C2×C3×D9 | C2×C4 | semidirect |
| 45. C9×Dic3 | C2×C4 | semidirect |
| 46. C3×Dic9 | D4 | semidirect |
| 89. Dic3⋊C4 | D9 | semidirect |
| 114. C2×D9 | C4×D3 | semidirect |
| 121. Dic9 | #67 | semidirect |
| 123. C3×C9 | C4×D4 | semidirect |
| 197. Dic3 | C4×D9 | semidirect |
| 200. C9 | C4×#67 | semidirect |
| 238. C3 | #63455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D9 | 2 |
| C2×#6192 | 2 |
| C2×(C3⋊D9)⋊C4 | 2 |
| #88536 | 2 |
| C9×Dic3⋊C4 | 2 |
| (C2×D9)⋊Dic3 | 2 |
| Dic3×Dic9 | 2 |
| #63904 | 3 |
| #63455 | 3 |