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. #31826816 | C2 | semidirect |
| 5. #31826775 | C2 | semidirect |
| 8. #31826675 | C2 | semidirect |
| 9. C8×Dic566 | C2 | semidirect |
| 10. #31826557 | C2 | semidirect |
| 115. C283 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827194 | 2 |
| #31827185 | 2 |
| #31826818 | 2 |
| #31826816 | 2 |
| #31826775 | 2 |
| #31826745 | 2 |
| #31826685 | 2 |
| #31826675 | 2 |
| C8×Dic566 | 2 |
| #31826557 | 2 |
| C4×SD16×C283 | 2 |
| #3364 | 283 |