Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
282 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 2. C3×C4×C3⋊Dic3 | C2 | semidirect |
| 3. C3×#3748 | C2 | semidirect |
| 10. C3×C4⋊(C3⋊D3) | C4 | semidirect |
| 12. C3×#634 | C4 | semidirect |
| 18. C4×C3⋊Dic3 | D3 | semidirect |
| 19. #3748 | D3 | semidirect |
| 44. C4⋊(C3⋊D3) | Dic3 | semidirect |
| 46. #634 | Dic3 | semidirect |
| 115. C33 | #104 | semidirect |
| 205. C32 | #805 | semidirect |
| 206. C32 | #825 | semidirect |
| 207. C32 | #837 | semidirect |
| 243. C3 | #63568 | semidirect |
| 244. C3 | #63569 | semidirect |
| 245. C3 | #63570 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3828 | 2 |
| C3×C4×C3⋊Dic3 | 2 |
| C3×#3748 | 2 |
| #63570 | 3 |
| #63569 | 3 |
| #63568 | 3 |