Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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. #31826513 | C2 | semidirect |
| 5. #31826237 | C2 | semidirect |
| 6. #31826225 | C2 | semidirect |
| 7. C4×M16×C283 | C2 | semidirect |
| 16. #22583528 | C4 | semidirect |
| 17. #22583526 | C4 | semidirect |
| 95. C283 | #1932 | semidirect |
| 101. C4×M16 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31826513 | 2 |
| #31826481 | 2 |
| C2×#22583538 | 2 |
| #31826447 | 2 |
| #31826237 | 2 |
| #31826225 | 2 |
| C4×M16×C283 | 2 |
| #1932 | 283 |