Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
568 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 104 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. #89076 | C2 | semidirect |
| 2. C2×C32×D12 | C2 | semidirect |
| 3. C3×#3748 | C2 | semidirect |
| 4. #88794 | C2 | semidirect |
| 5. #88790 | C2 | semidirect |
| 11. C4⋊(C3⋊(C3⋊D3)) | C22 | semidirect |
| 13. #6308 | C22 | semidirect |
| 16. C3×C3⋊(C3⋊C8) | C22 | semidirect |
| 21. C2×C3×D12 | D3 | semidirect |
| 24. #3748 | D3 | semidirect |
| 58. C3⋊(C3⋊C8) | C2×D3 | semidirect |
| 68. C2×D12 | C3⋊D3 | semidirect |
| 95. C33 | AGL(1,ℤ/8) | semidirect |
| 155. C32 | #908 | semidirect |
| 156. C32 | #932 | semidirect |
| 185. C3 | #63830 | semidirect |
| 186. C3 | #64141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #89076 | 2 |
| C2×C32×D12 | 2 |
| C3×#3748 | 2 |
| #88794 | 2 |
| #88790 | 2 |
| #64141 | 3 |
| #63830 | 3 |