Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 350 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. #31827185 | C2 | semidirect |
| 2. #31827172 | C2 | semidirect |
| 3. #31826818 | C2 | semidirect |
| 4. #31826816 | C2 | semidirect |
| 5. #31826771 | C2 | semidirect |
| 6. #31826755 | C2 | semidirect |
| 8. #31826670 | C2 | semidirect |
| 9. C8×Dic566 | C2 | semidirect |
| 10. #31826556 | C2 | semidirect |
| 120. C283 | #3360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827185 | 2 |
| #31827172 | 2 |
| #31826818 | 2 |
| #31826816 | 2 |
| #31826771 | 2 |
| #31826755 | 2 |
| #31826678 | 2 |
| #31826670 | 2 |
| C8×Dic566 | 2 |
| #31826556 | 2 |
| C4×D8×C283 | 2 |
| #3360 | 283 |