Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
398 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 149 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. #31827093 | C2 | semidirect |
| 2. #31826765 | C2 | semidirect |
| 3. #31826765 | C2 | semidirect |
| 4. #31826755 | C2 | semidirect |
| 5. #31826745 | C2 | semidirect |
| 6. #31826508 | C2 | semidirect |
| 7. #31826501 | C2 | semidirect |
| 8. #31826492 | C2 | semidirect |
| 14. #22583610 | C22 | semidirect |
| 16. #22583602 | C22 | 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 |
| 60. C2×D4×C283 | Q8 | semidirect |
| 124. C283 | #3081 | semidirect |
| 170. C2×D4 | Dic566 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827093 | 2 |
| #31826765 | 2 |
| #31826755 | 2 |
| #31826745 | 2 |
| #31826508 | 2 |
| #31826501 | 2 |
| #31826492 | 2 |
| #31826470 | 2 |
| C2×#22583531 | 2 |
| #518×C283 | 2 |
| #3081 | 283 |