Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
239 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 239 conjugacy classes of subgroups — too many to draw. Only its 67 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. #3828⋊C3 | C2 | semidirect |
| 2. C2×C8×H(3,𝔽3) | C2 | semidirect |
| 3. #3745⋊C3 | C2 | semidirect |
| 4. #3744⋊C3 | C2 | semidirect |
| 5. #3746⋊C3 | C2 | semidirect |
| 6. #64113 | C3 | semidirect |
| 15. #3828 | C2×C3 | semidirect |
| 18. C2×C32×C8 | D3 | semidirect |
| 19. C2×C32×C8 | C2×C3 | semidirect |
| 20. #3746 | C2×C3 | semidirect |
| 21. #3745 | C2×C3 | semidirect |
| 22. #3744 | C2×C3 | semidirect |
| 84. H(3,𝔽3) | #135 | semidirect |
| 121. C2×C8 | (C3⋊D3)⋊C3 | semidirect |
| 141. C32 | #904 | semidirect |
| 142. C32 | C3×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3828⋊C3 | 2 |
| C2×C8×H(3,𝔽3) | 2 |
| #3745⋊C3 | 2 |
| #3744⋊C3 | 2 |
| #3746⋊C3 | 2 |
| #64113 | 3 |
| C3×#904 | 3 |