Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
354 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 354 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 |
|---|---|---|
| 2. C2×C3×#634 | C2 | semidirect |
| 3. C3×#3748 | C2 | semidirect |
| 4. #88812 | C2 | semidirect |
| 5. #88811 | C2 | semidirect |
| 19. C2×#634 | D3 | semidirect |
| 26. #3748 | D3 | semidirect |
| 139. C33 | #137 | semidirect |
| 239. C32 | #909 | semidirect |
| 240. C32 | #942 | semidirect |
| 241. C32 | #951 | semidirect |
| 279. C3 | #63827 | semidirect |
| 280. C3 | #63831 | semidirect |
| 281. C3 | #63833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3828 | 2 |
| C2×C3×#634 | 2 |
| C3×#3748 | 2 |
| #88812 | 2 |
| #88811 | 2 |
| #63833 | 3 |
| #63831 | 3 |
| #63827 | 3 |