Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
120 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 47 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. #31826867 | C2 | semidirect |
| 3. #31826288 | C2 | semidirect |
| 5. #364×C283 | C2 | semidirect |
| 50. C283 | #2231 | semidirect |
| 55. #364 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31826867 | 2 |
| #31826583 | 2 |
| #31826288 | 2 |
| #31826276 | 2 |
| #364×C283 | 2 |
| #2231 | 283 |