Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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×Q16×D283 | C2 | semidirect |
| 4. #31826724 | C2 | semidirect |
| 5. #31826723 | C2 | semidirect |
| 6. #31826720 | C2 | semidirect |
| 7. #31826705 | C2 | semidirect |
| 8. #31826704 | C2 | semidirect |
| 9. #31826500 | C2 | semidirect |
| 10. #31826472 | C2 | semidirect |
| 11. #470×C283 | C2 | semidirect |
| 133. C283 | #3059 | semidirect |
| 141. #470 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D283 | 2 |
| C2×#22583618 | 2 |
| #31827038 | 2 |
| #31826724 | 2 |
| #31826723 | 2 |
| #31826720 | 2 |
| #31826705 | 2 |
| #31826704 | 2 |
| #31826500 | 2 |
| #31826472 | 2 |
| #470×C283 | 2 |
| #3059 | 283 |