Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
346 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 346 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 |
|---|---|---|
| 1. C3×#3750 | C2 | semidirect |
| 3. C32×C4×Dic3 | C2 | semidirect |
| 4. C3×#3724 | C2 | semidirect |
| 5. C3×Dic3⋊Dic3 | C2 | semidirect |
| 10. #63859 | C3 | direct (N × H) |
| 20. #3750 | C2×C3 | semidirect |
| 36. C3×C4×Dic3 | D3 | semidirect |
| 37. C3×C4×Dic3 | C2×C3 | semidirect |
| 38. #3724 | C2×C3 | semidirect |
| 39. Dic3⋊Dic3 | C2×C3 | semidirect |
| 113. C4×Dic3 | C3×D3 | semidirect |
| 161. C33 | #126 | semidirect |
| 275. C32 | #876 | semidirect |
| 276. C32 | #879 | semidirect |
| 277. C32 | C3×#126 | semidirect |
| 324. C3 | #63859 | direct (N × H) |
| 325. C3 | C3×#876 | semidirect |
| 326. C3 | C3×#879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3750 | 2 |
| C32×(C2×D3)⋊C4 | 2 |
| C32×C4×Dic3 | 2 |
| C3×#3724 | 2 |
| C3×Dic3⋊Dic3 | 2 |
| C3×(C2×D3)⋊Dic3 | 2 |
| C3×#879 | 3 |
| C3×#876 | 3 |
| #63859 | 3 |