Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #31827096 | C2 | semidirect |
| 3. #31826774 | C2 | semidirect |
| 4. #31826763 | C2 | semidirect |
| 5. #31826753 | C2 | semidirect |
| 6. #31826748 | C2 | semidirect |
| 7. #31826507 | C2 | semidirect |
| 8. C2×#22583541 | C2 | semidirect |
| 9. #31826493 | C2 | semidirect |
| 64. #41×C283 | Q8 | semidirect |
| 123. C283 | #3084 | semidirect |
| 166. #41 | Dic566 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827096 | 2 |
| #31826948 | 2 |
| #31826774 | 2 |
| #31826763 | 2 |
| #31826753 | 2 |
| #31826748 | 2 |
| #31826507 | 2 |
| C2×#22583541 | 2 |
| #31826493 | 2 |
| #31826461 | 2 |
| #417×C283 | 2 |
| #3084 | 283 |