Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
370 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 129 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. #31827270 | C2 | semidirect |
| 2. #31826901 | C2 | semidirect |
| 3. #31826900 | C2 | semidirect |
| 4. #31826895 | C2 | semidirect |
| 5. C2×#22583551 | C2 | semidirect |
| 6. #31826882 | C2 | semidirect |
| 7. #576×C283 | C2 | semidirect |
| 10. #22583632 | C22 | semidirect |
| 11. C2×D2264 | C22 | semidirect |
| 12. #22583556 | C22 | semidirect |
| 13. #22583554 | C22 | semidirect |
| 14. #22583553 | C22 | semidirect |
| 15. #22583551 | C22 | semidirect |
| 16. #22583551 | C22 | semidirect |
| 17. #22583550 | C22 | semidirect |
| 18. C2×C283⋊C16 | C22 | semidirect |
| 21. #135×C283 | C22 | semidirect |
| 22. C2×D8×C283 | C22 | semidirect |
| 75. C283 | #3415 | semidirect |
| 78. #576 | D283 | semidirect |
| 89. #135 | C2×D283 | semidirect |
| 91. C2×D8 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827270 | 2 |
| #31826901 | 2 |
| #31826900 | 2 |
| #31826895 | 2 |
| C2×#22583551 | 2 |
| #31826882 | 2 |
| #576×C283 | 2 |
| #3415 | 283 |