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. C2×C33×D4 | C2 | semidirect |
| 2. #89076 | C2 | semidirect |
| 3. #88861 | C2 | semidirect |
| 4. #88860 | C2 | semidirect |
| 5. #88855 | C2 | semidirect |
| 12. C4⋊(C3⋊(C3⋊D3)) | C22 | semidirect |
| 14. #6308 | C22 | semidirect |
| 15. C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 16. C2×C32×D4 | D3 | semidirect |
| 42. C2×C3×D4 | C3⋊D3 | semidirect |
| 55. C33 | AGL(1,ℤ/8) | semidirect |
| 70. C2×D4 | C3⋊(C3⋊D3) | semidirect |
| 81. C32 | #932 | semidirect |
| 102. C3 | #64141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D4 | 2 |
| #89076 | 2 |
| #88861 | 2 |
| #88860 | 2 |
| #88855 | 2 |
| #64141 | 3 |