Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 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. #31826939 | C2 | semidirect |
| 3. #31826575 | C2 | semidirect |
| 4. C4×#17985377 | C2 | semidirect |
| 5. #31826501 | C2 | semidirect |
| 6. #31826470 | C2 | semidirect |
| 7. #31826469 | C2 | semidirect |
| 8. #31826421 | C2 | semidirect |
| 9. #518×C283 | C2 | semidirect |
| 11. C2×#17985377 | C4 | semidirect |
| 16. C4×D1132 | C22 | semidirect |
| 20. #22583543 | C22 | semidirect |
| 21. #22583541 | C22 | semidirect |
| 22. #22583531 | C22 | semidirect |
| 23. #22583530 | C22 | semidirect |
| 24. #22583521 | C22 | semidirect |
| 25. C4×C283⋊C8 | C22 | semidirect |
| 28. C4×D4×C283 | C22 | semidirect |
| 35. C2×D1132 | C2×C4 | semidirect |
| 38. #17985377 | C2×C4 | semidirect |
| 39. #17985377 | C2×C4 | semidirect |
| 41. C2×C283⋊C8 | C2×C4 | semidirect |
| 52. C2×D4×C283 | C2×C4 | semidirect |
| 108. C283 | #2948 | semidirect |
| 112. #518 | D283 | semidirect |
| 129. C4×D4 | C2×D283 | semidirect |
| 149. C2×D4 | C4×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17985377 | 2 |
| #31826939 | 2 |
| #31826575 | 2 |
| C4×#17985377 | 2 |
| #31826501 | 2 |
| #31826470 | 2 |
| #31826469 | 2 |
| #31826421 | 2 |
| #518×C283 | 2 |
| #2948 | 283 |