Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
456 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 177 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. C2×#22583618 | C2 | semidirect |
| 3. #31826586 | C2 | semidirect |
| 4. #31826581 | C2 | semidirect |
| 5. #31826481 | C2 | semidirect |
| 6. #31826423 | C2 | semidirect |
| 7. #430×C283 | C2 | semidirect |
| 9. #22583643 | C4 | semidirect |
| 10. #22583638 | C4 | semidirect |
| 14. #22583618 | C22 | semidirect |
| 15. #22583618 | C22 | semidirect |
| 20. #22583536 | C22 | semidirect |
| 21. #22583520 | C22 | semidirect |
| 22. C8×Dic283 | C22 | semidirect |
| 25. #108×C283 | C22 | semidirect |
| 89. C283 | #2955 | semidirect |
| 95. #430 | D283 | semidirect |
| 112. #108 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827265 | 2 |
| C2×#22583618 | 2 |
| #31826586 | 2 |
| #31826581 | 2 |
| #31826481 | 2 |
| #31826423 | 2 |
| #430×C283 | 2 |
| #2955 | 283 |