Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 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 |
|---|---|---|
| 1. C2×#22583616 | C2 | semidirect |
| 2. #31827032 | C2 | semidirect |
| 3. #31826715 | C2 | semidirect |
| 4. #31826698 | C2 | semidirect |
| 5. #31826503 | C2 | semidirect |
| 6. #31826470 | C2 | semidirect |
| 7. C22×D8×C283 | C2 | semidirect |
| 11. C2×#17985375 | C22 | semidirect |
| 12. C2×C8×D283 | C22 | semidirect |
| 15. #22583581 | C22 | semidirect |
| 18. #22583544 | C22 | semidirect |
| 19. #22583542 | C22 | semidirect |
| 20. #22583531 | C22 | semidirect |
| 49. C2×C8×C283 | D4 | semidirect |
| 93. C283 | #3058 | semidirect |
| 95. C22×D8 | D283 | semidirect |
| 139. C2×C8 | C22⋊D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583616 | 2 |
| #31827032 | 2 |
| #31826715 | 2 |
| #31826698 | 2 |
| #31826503 | 2 |
| #31826470 | 2 |
| C22×D8×C283 | 2 |
| #3058 | 283 |