Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#22583636 | C2 | semidirect |
| 2. #31827015 | C2 | semidirect |
| 3. #31826852 | C2 | semidirect |
| 4. #31826841 | C2 | semidirect |
| 5. #31826837 | C2 | semidirect |
| 6. C4×#17985376 | C2 | semidirect |
| 7. C2×#127×C283 | C2 | semidirect |
| 10. C2×#17985380 | C22 | semidirect |
| 11. C2×#17985377 | C22 | semidirect |
| 13. #22583610 | C22 | semidirect |
| 14. #22583607 | C22 | semidirect |
| 15. #22583598 | C22 | semidirect |
| 18. #22583521 | C22 | semidirect |
| 19. C4×C283⋊C8 | C22 | semidirect |
| 34. #17985376 | D4 | semidirect |
| 57. C283⋊C8 | C2×D4 | semidirect |
| 82. C4×C283 | AGL(1,ℤ/8) | semidirect |
| 90. C283 | #3151 | semidirect |
| 94. C2×#127 | D283 | semidirect |
| 174. C4 | #22583636 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583636 | 2 |
| #31827015 | 2 |
| #31826852 | 2 |
| #31826841 | 2 |
| #31826837 | 2 |
| C4×#17985376 | 2 |
| C2×#127×C283 | 2 |
| #3151 | 283 |