Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
354 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 88 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×C32×Dic6 | C2 | semidirect |
| 3. C3×#3748 | C2 | semidirect |
| 4. C3×#3718 | C2 | semidirect |
| 5. C3×#3715 | C2 | semidirect |
| 8. #63827 | C3 | direct (N × H) |
| 24. C2×C3×Dic6 | D3 | semidirect |
| 25. C2×C3×Dic6 | C2×C3 | semidirect |
| 26. #3748 | C2×C3 | semidirect |
| 34. #3718 | C2×C3 | semidirect |
| 35. #3715 | C2×C3 | semidirect |
| 94. C2×Dic6 | C3×D3 | semidirect |
| 139. C33 | #137 | semidirect |
| 239. C32 | #942 | semidirect |
| 240. C32 | #951 | semidirect |
| 241. C32 | C3×#137 | semidirect |
| 279. C3 | #63827 | direct (N × H) |
| 280. C3 | C3×#942 | semidirect |
| 281. C3 | C3×#951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#235 | 2 |
| C2×C32×Dic6 | 2 |
| C3×#3748 | 2 |
| C3×#3718 | 2 |
| C3×#3715 | 2 |
| C3×#951 | 3 |
| C3×#942 | 3 |
| #63827 | 3 |