Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
336 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31827194 | C2 | semidirect |
| 4. #31826815 | C2 | semidirect |
| 5. #31826774 | C2 | semidirect |
| 8. #31826589 | C2 | semidirect |
| 9. Q16×Dic283 | C2 | semidirect |
| 11. #462×C283 | C2 | semidirect |
| 115. C283 | #3364 | semidirect |
| 124. #462 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827194 | 2 |
| #31827189 | 2 |
| #31826821 | 2 |
| #31826815 | 2 |
| #31826774 | 2 |
| #31826746 | 2 |
| #31826689 | 2 |
| #31826589 | 2 |
| Q16×Dic283 | 2 |
| C4×#17985379 | 2 |
| #462×C283 | 2 |
| #3364 | 283 |