Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
952 conjugacy classes of subgroups; only the 263 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 263 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×C4⋊(C3⋊(C3⋊D3)) | C2 | semidirect |
| 3. C33×M16 | C2 | semidirect |
| 4. #88852 | C2 | semidirect |
| 5. #88851 | C2 | semidirect |
| 12. C4⋊(C3⋊(C3⋊D3)) | C22 | semidirect |
| 14. #6308 | C22 | semidirect |
| 15. C33×C8 | C22 | semidirect |
| 18. C32×M16 | D3 | semidirect |
| 37. C32×C8 | C2×D3 | semidirect |
| 44. C3×M16 | C3⋊D3 | semidirect |
| 55. C33 | AGL(1,ℤ/8) | semidirect |
| 64. C3×C8 | C2×C3⋊D3 | semidirect |
| 73. M16 | C3⋊(C3⋊D3) | semidirect |
| 81. C32 | #908 | semidirect |
| 90. C8 | C2×C3⋊(C3⋊D3) | semidirect |
| 102. C3 | #64117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #89076 | 2 |
| C2×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C33×M16 | 2 |
| #88852 | 2 |
| #88851 | 2 |
| #64117 | 3 |