Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
426 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31827130 | C2 | semidirect |
| 3. #31826813 | C2 | semidirect |
| 4. #31826810 | C2 | semidirect |
| 5. #31826744 | C2 | semidirect |
| 6. #31826661 | C2 | semidirect |
| 7. #31826659 | C2 | semidirect |
| 8. #31826589 | C2 | semidirect |
| 9. #31826547 | C2 | semidirect |
| 10. C4×#17985377 | C2 | semidirect |
| 11. #474×C283 | C2 | semidirect |
| 78. Dic566 | D8 | semidirect |
| 84. D1132 | #41 | semidirect |
| 131. C283 | #3358 | semidirect |
| 138. #474 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827136 | 2 |
| #31827130 | 2 |
| #31826813 | 2 |
| #31826810 | 2 |
| #31826744 | 2 |
| #31826661 | 2 |
| #31826659 | 2 |
| #31826589 | 2 |
| #31826547 | 2 |
| C4×#17985377 | 2 |
| #474×C283 | 2 |
| #3358 | 283 |