Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
426 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 96 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×C32×Dic6 | C2 | semidirect |
| 3. C3×#3752 | C2 | semidirect |
| 4. C32×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C3×#3722 | C2 | semidirect |
| 6. C3×(C2×D3)⋊Dic3 | C2 | semidirect |
| 7. C3×Dic32 | C2 | semidirect |
| 10. #63907 | C3 | direct (N × H) |
| 24. C2×C3×Dic6 | D3 | semidirect |
| 25. C2×C3×Dic6 | C2×C3 | semidirect |
| 28. #3752 | C2×C3 | semidirect |
| 37. C3×(C2×D3)⋊C4 | D3 | semidirect |
| 38. C3×(C2×D3)⋊C4 | C2×C3 | semidirect |
| 41. #3722 | C2×C3 | semidirect |
| 42. (C2×D3)⋊Dic3 | C2×C3 | semidirect |
| 43. Dic32 | C2×C3 | semidirect |
| 108. C2×Dic6 | C3×D3 | semidirect |
| 123. (C2×D3)⋊C4 | C3×D3 | semidirect |
| 181. C33 | #124 | semidirect |
| 314. C32 | #885 | semidirect |
| 315. C32 | #947 | semidirect |
| 316. C32 | C3×#124 | semidirect |
| 371. C3 | #63907 | direct (N × H) |
| 372. C3 | C3×#885 | semidirect |
| 373. C3 | C3×#947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Dic6 | 2 |
| C2×C3×#626 | 2 |
| C3×#3752 | 2 |
| C32×(C2×D3)⋊C4 | 2 |
| C3×#3722 | 2 |
| C3×(C2×D3)⋊Dic3 | 2 |
| C3×Dic32 | 2 |
| C3×#947 | 3 |
| C3×#885 | 3 |
| #63907 | 3 |