Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
460 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 110 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×#3830 | C2 | semidirect |
| 2. C33×D8 | C2 | semidirect |
| 3. C3×#3754 | C2 | semidirect |
| 4. C3×#3746 | C2 | semidirect |
| 5. C3×C8×C3⋊D3 | C2 | semidirect |
| 6. #64121 | C3 | direct (N × H) |
| 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 |
| 57. C3×D8 | C3×D3 | semidirect |
| 58. C3×D8 | C3⋊D3 | semidirect |
| 76. C33 | #135 | semidirect |
| 104. D8 | C3×C3⋊D3 | semidirect |
| 119. C32 | #912 | semidirect |
| 120. C32 | C3×#135 | semidirect |
| 142. C3 | C3×#912 | semidirect |
| 143. C3 | #64121 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3830 | 2 |
| C33×D8 | 2 |
| C3×#3754 | 2 |
| C3×#3746 | 2 |
| C3×C8×C3⋊D3 | 2 |
| #64121 | 3 |
| C3×#912 | 3 |