Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #31827022 | C2 | semidirect |
| 2. #31826824 | C2 | semidirect |
| 3. #31826819 | C2 | semidirect |
| 4. #31826474 | C2 | semidirect |
| 6. C4×#17985376 | C2 | semidirect |
| 9. #22583610 | C22 | semidirect |
| 10. #22583602 | C22 | semidirect |
| 14. #22583534 | C22 | semidirect |
| 16. #22583521 | C22 | semidirect |
| 17. C4×C283⋊C8 | C22 | semidirect |
| 83. C283 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827022 | 2 |
| #31826824 | 2 |
| #31826819 | 2 |
| #31826474 | 2 |
| #31826470 | 2 |
| C4×#17985376 | 2 |
| C2×#124×C283 | 2 |
| #3140 | 283 |