Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 2. #31826789 | C2 | semidirect |
| 3. #31826789 | C2 | semidirect |
| 4. #31826783 | C2 | semidirect |
| 5. #31826778 | C2 | semidirect |
| 6. #31826505 | C2 | semidirect |
| 7. #31826501 | C2 | semidirect |
| 8. #31826469 | C2 | semidirect |
| 9. C2×#22583530 | C2 | semidirect |
| 10. #31826432 | C2 | semidirect |
| 11. #520×C283 | C2 | semidirect |
| 21. #22583543 | C22 | semidirect |
| 22. #22583543 | C22 | semidirect |
| 23. #22583543 | C22 | semidirect |
| 24. #22583541 | C22 | semidirect |
| 25. #22583541 | C22 | semidirect |
| 26. #22583541 | C22 | semidirect |
| 31. C22⋊(C283⋊C8) | C22 | semidirect |
| 32. C22⋊(C283⋊C8) | C22 | semidirect |
| 38. #117×C283 | C22 | semidirect |
| 40. C2×C4⋊C4×C283 | C22 | semidirect |
| 134. C283 | #3096 | semidirect |
| 137. #520 | D283 | semidirect |
| 161. #117 | C2×D283 | semidirect |
| 163. C2×C4⋊C4 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827029 | 2 |
| #31826789 | 2 |
| #31826783 | 2 |
| #31826778 | 2 |
| #31826505 | 2 |
| #31826501 | 2 |
| #31826469 | 2 |
| C2×#22583530 | 2 |
| #31826432 | 2 |
| #520×C283 | 2 |
| #3096 | 283 |