Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
492 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 145 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. #31827015 | C2 | semidirect |
| 2. #31826778 | C2 | semidirect |
| 3. #31826745 | C2 | semidirect |
| 4. #31826660 | C2 | semidirect |
| 5. #31826599 | C2 | semidirect |
| 6. C4×#17985377 | C2 | semidirect |
| 7. #31826518 | C2 | semidirect |
| 8. C2×C4×D4×C283 | C2 | semidirect |
| 11. #22583610 | C22 | semidirect |
| 12. #22583607 | C22 | semidirect |
| 17. C4×D1132 | C22 | semidirect |
| 18. #22583543 | C22 | semidirect |
| 19. C4⋊(C283⋊C8) | C22 | semidirect |
| 21. #22583530 | C22 | semidirect |
| 23. C4×C283⋊C8 | C22 | semidirect |
| 81. D4×C283 | #41 | semidirect |
| 88. C2×C4×C283 | D8 | semidirect |
| 120. C283 | #3100 | semidirect |
| 123. C2×C4×D4 | D283 | semidirect |
| 199. D4 | #17985392 | semidirect |
| 208. C2×C4 | #17985377 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827015 | 2 |
| #31826778 | 2 |
| #31826745 | 2 |
| #31826660 | 2 |
| #31826599 | 2 |
| C4×#17985377 | 2 |
| #31826518 | 2 |
| C2×C4×D4×C283 | 2 |
| #3100 | 283 |