Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
306 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 3. C32×Dic12 | C2 | semidirect |
| 4. C3×#3718 | C2 | semidirect |
| 6. #63802 | C3 | direct (N × H) |
| 19. C3×Dic12 | D3 | semidirect |
| 20. C3×Dic12 | C2×C3 | semidirect |
| 23. #3718 | C2×C3 | semidirect |
| 50. C3×C3⋊D3 | Q16 | semidirect |
| 59. Dic12 | C3×D3 | semidirect |
| 78. C33 | C2×Q16 | semidirect |
| 103. C3⋊D3 | C3×Q16 | semidirect |
| 128. C32 | D3×Q16 | semidirect |
| 129. C32 | C2×C3×Q16 | semidirect |
| 151. C3 | #63802 | direct (N × H) |
| 152. C3 | C3×D3×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3797 | 2 |
| C3×C8×C3⋊D3 | 2 |
| C32×Dic12 | 2 |
| C3×#3718 | 2 |
| C3×D3×Q16 | 3 |
| #63802 | 3 |