Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31827282 | C2 | semidirect |
| 2. #31827279 | C2 | semidirect |
| 3. #31826845 | C2 | semidirect |
| 4. #31826741 | C2 | semidirect |
| 5. #31826740 | C2 | semidirect |
| 6. #31826649 | C2 | semidirect |
| 7. #31826583 | C2 | semidirect |
| 8. #443×C283 | C2 | semidirect |
| 99. C283 | #3293 | semidirect |
| 108. #443 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827282 | 2 |
| #31827279 | 2 |
| #31826845 | 2 |
| #31826741 | 2 |
| #31826740 | 2 |
| #31826649 | 2 |
| #31826583 | 2 |
| #443×C283 | 2 |
| #3293 | 283 |