Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
300 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 300 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 |
|---|---|---|
| 3. #31826421 | C2 | semidirect |
| 4. C2×C8×Dic283 | C2 | semidirect |
| 5. #31826230 | C2 | semidirect |
| 6. #31826224 | C2 | semidirect |
| 9. #22583617 | C4 | semidirect |
| 16. #22583537 | C4 | semidirect |
| 23. #103×C283 | C4 | semidirect |
| 24. #102×C283 | C4 | semidirect |
| 98. C283 | #1764 | semidirect |
| 119. #103 | Dic283 | semidirect |
| 120. #102 | Dic283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583617 | 2 |
| C2×#22583537 | 2 |
| #31826421 | 2 |
| C2×C8×Dic283 | 2 |
| #31826230 | 2 |
| #31826224 | 2 |
| #416×C283 | 2 |
| #1764 | 283 |