Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
1088 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 341 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. C2×#22583569 | C2 | semidirect |
| 2. #31826328 | C2 | semidirect |
| 3. #31826325 | C2 | semidirect |
| 5. C4×C22⋊Dic283 | C2 | semidirect |
| 8. C2×C4⋊Dic283 | C22 | semidirect |
| 11. C2×C4×Dic283 | C22 | semidirect |
| 12. C283⋊#95 | C22 | semidirect |
| 15. C23×C4×C283 | C4 | semidirect |
| 59. C2×C4×C283 | C22⋊C4 | semidirect |
| 72. C22×C283 | #117 | semidirect |
| 85. C283 | #2280 | semidirect |
| 95. C23×C4 | Dic283 | semidirect |
| 145. C2×C4 | C22⋊Dic283 | semidirect |
| 158. C22 | #22583569 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583569 | 2 |
| #31826328 | 2 |
| #31826325 | 2 |
| #31826321 | 2 |
| C4×C22⋊Dic283 | 2 |
| C24×C4×C283 | 2 |
| #2280 | 283 |