Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31827136 | C2 | semidirect |
| 2. D4×Dic566 | C2 | semidirect |
| 3. #31826812 | C2 | semidirect |
| 4. #31826810 | C2 | semidirect |
| 5. #31826745 | C2 | semidirect |
| 6. #31826744 | C2 | semidirect |
| 7. #31826660 | C2 | semidirect |
| 8. #31826658 | C2 | semidirect |
| 9. C8×Dic566 | C2 | semidirect |
| 10. #31826545 | C2 | semidirect |
| 11. C4×D8×C283 | C2 | semidirect |
| 78. Dic566 | D8 | semidirect |
| 96. D4×C283 | #41 | semidirect |
| 131. C283 | #3358 | semidirect |
| 143. C4×D8 | D283 | semidirect |
| 222. D4 | #17985392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827136 | 2 |
| D4×Dic566 | 2 |
| #31826812 | 2 |
| #31826810 | 2 |
| #31826745 | 2 |
| #31826744 | 2 |
| #31826660 | 2 |
| #31826658 | 2 |
| C8×Dic566 | 2 |
| #31826545 | 2 |
| C4×D8×C283 | 2 |
| #3358 | 283 |