Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. C4⋊Q8×D283 | C2 | semidirect |
| 3. #31826827 | C2 | semidirect |
| 4. #31826825 | C2 | semidirect |
| 5. #31826824 | C2 | semidirect |
| 6. #31826814 | C2 | semidirect |
| 7. #31826810 | C2 | semidirect |
| 8. #31826465 | C2 | semidirect |
| 9. #31826463 | C2 | semidirect |
| 10. #31826417 | C2 | semidirect |
| 11. #489×C283 | C2 | semidirect |
| 140. C283 | #3141 | semidirect |
| 147. #489 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827014 | 2 |
| C4⋊Q8×D283 | 2 |
| #31826827 | 2 |
| #31826825 | 2 |
| #31826824 | 2 |
| #31826814 | 2 |
| #31826810 | 2 |
| #31826465 | 2 |
| #31826463 | 2 |
| #31826417 | 2 |
| #489×C283 | 2 |
| #3141 | 283 |