Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
402 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 197 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. #31826543 | C2 | semidirect |
| 2. #31826537 | C2 | semidirect |
| 3. #31826526 | C2 | semidirect |
| 4. #31826432 | C2 | semidirect |
| 5. #31826429 | C2 | semidirect |
| 8. C2×#17985376 | C22 | semidirect |
| 9. C22×C283⋊C8 | C22 | semidirect |
| 10. C4⋊(C283⋊C8) | C22 | semidirect |
| 14. C22⋊(C283⋊C8) | C22 | semidirect |
| 15. #22583521 | C22 | semidirect |
| 16. C4×C283⋊C8 | C22 | semidirect |
| 89. C283 | #2978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31826543 | 2 |
| #31826537 | 2 |
| #31826526 | 2 |
| #31826432 | 2 |
| #31826429 | 2 |
| #525×C283 | 2 |
| #2978 | 283 |