Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
464 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 104 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. #88857 | C2 | semidirect |
| 2. C3×C4×C3⋊Dic3 | C2 | semidirect |
| 4. #88806 | C2 | semidirect |
| 5. Dic3⋊(C3⋊Dic3) | C2 | semidirect |
| 25. C4×C3⋊Dic3 | D3 | semidirect |
| 105. C33 | #126 | semidirect |
| 166. C32 | #876 | semidirect |
| 167. C32 | #879 | semidirect |
| 197. C3 | #63859 | semidirect |
| 198. C3 | #64088 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #88857 | 2 |
| C3×C4×C3⋊Dic3 | 2 |
| C32×(C2×D3)⋊C4 | 2 |
| #88806 | 2 |
| Dic3⋊(C3⋊Dic3) | 2 |
| (C2×D3)⋊(C3⋊Dic3) | 2 |
| #64088 | 3 |
| #63859 | 3 |