Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
239 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 239 conjugacy classes of subgroups — too many to draw. Only its 61 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. #3830⋊C3 | C2 | semidirect |
| 2. D8×H(3,𝔽3) | C2 | semidirect |
| 3. #3754⋊C3 | C2 | semidirect |
| 4. C8×(C3⋊D3)⋊C3 | C2 | semidirect |
| 5. #3746⋊C3 | C2 | semidirect |
| 6. #64121 | C3 | semidirect |
| 15. #3830 | C2×C3 | semidirect |
| 18. C32×D8 | D3 | semidirect |
| 19. C32×D8 | C2×C3 | semidirect |
| 20. #3754 | C2×C3 | semidirect |
| 21. #3746 | C2×C3 | semidirect |
| 22. C8×C3⋊D3 | C2×C3 | semidirect |
| 82. H(3,𝔽3) | #135 | semidirect |
| 117. D8 | (C3⋊D3)⋊C3 | semidirect |
| 137. C32 | #912 | semidirect |
| 138. C32 | C3×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3830⋊C3 | 2 |
| D8×H(3,𝔽3) | 2 |
| #3754⋊C3 | 2 |
| C8×(C3⋊D3)⋊C3 | 2 |
| #3746⋊C3 | 2 |
| #64121 | 3 |
| C3×#912 | 3 |