Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #31826762 | C2 | semidirect |
| 3. #31826762 | C2 | semidirect |
| 4. #31826752 | C2 | semidirect |
| 5. #31826742 | C2 | semidirect |
| 6. #31826505 | C2 | semidirect |
| 7. #31826501 | C2 | semidirect |
| 8. #31826492 | C2 | semidirect |
| 11. #544×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 |
| 27. C4⋊(C283⋊C8) | C22 | semidirect |
| 28. C4⋊(C283⋊C8) | C22 | semidirect |
| 34. C4⋊Q8×C283 | C22 | semidirect |
| 36. #125×C283 | C22 | semidirect |
| 44. C2×D1132 | Q8 | semidirect |
| 124. C283 | #3081 | semidirect |
| 126. #544 | D283 | semidirect |
| 141. C4⋊Q8 | C2×D283 | semidirect |
| 143. #125 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31826939 | 2 |
| #31826762 | 2 |
| #31826752 | 2 |
| #31826742 | 2 |
| #31826505 | 2 |
| #31826501 | 2 |
| #31826492 | 2 |
| #31826469 | 2 |
| C2×#22583530 | 2 |
| #544×C283 | 2 |
| #3081 | 283 |