Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×Dic566 | C2 | semidirect |
| 3. #31826816 | C2 | semidirect |
| 4. #31826796 | C2 | semidirect |
| 5. #31826751 | C2 | semidirect |
| 6. #31826694 | C2 | semidirect |
| 7. #31826671 | C2 | semidirect |
| 8. #31826606 | C2 | semidirect |
| 9. C4×#17985381 | C2 | semidirect |
| 10. C2×#22583535 | C2 | semidirect |
| 11. C8×D4×C283 | C2 | semidirect |
| 83. Dic566 | #41 | semidirect |
| 96. D4×C283 | SD16 | semidirect |
| 128. C283 | #3298 | semidirect |
| 139. C8×D4 | D283 | semidirect |
| 217. D4 | #17985381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic566 | 2 |
| #31827119 | 2 |
| #31826816 | 2 |
| #31826796 | 2 |
| #31826751 | 2 |
| #31826694 | 2 |
| #31826671 | 2 |
| #31826606 | 2 |
| C4×#17985381 | 2 |
| C2×#22583535 | 2 |
| C8×D4×C283 | 2 |
| #3298 | 283 |