Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
318 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 76 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×#3796 | C2 | semidirect |
| 2. C3×C8×C3⋊D3 | C2 | semidirect |
| 3. C32×#204 | C2 | semidirect |
| 4. C3×#3718 | C2 | semidirect |
| 5. C3×#3713 | C2 | semidirect |
| 7. #63809 | C3 | direct (N × H) |
| 17. #3796 | C2×C3 | semidirect |
| 19. C8×C3⋊D3 | C2×C3 | semidirect |
| 23. C3×#204 | D3 | semidirect |
| 24. C3×#204 | C2×C3 | semidirect |
| 27. #3718 | C2×C3 | semidirect |
| 28. #3713 | C2×C3 | semidirect |
| 75. #204 | C3×D3 | semidirect |
| 98. C33 | #135 | semidirect |
| 163. C32 | #916 | semidirect |
| 164. C32 | C3×#135 | semidirect |
| 192. C3 | #63809 | direct (N × H) |
| 193. C3 | C3×#916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3796 | 2 |
| C3×C8×C3⋊D3 | 2 |
| C32×#204 | 2 |
| C3×#3718 | 2 |
| C3×#3713 | 2 |
| C3×#916 | 3 |
| #63809 | 3 |