Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
992 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 171 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. #24918474 | C2 | semidirect |
| 2. #24917808 | C2 | semidirect |
| 3. #24906769 | C2 | semidirect |
| 4. #24906098 | C2 | semidirect |
| 5. #24906074 | C2 | semidirect |
| 7. #19128258 | C22 | semidirect |
| 8. #19128096 | C22 | semidirect |
| 11. #19128060 | C22 | semidirect |
| 12. #19128060 | C22 | semidirect |
| 16. #19127758 | C22 | semidirect |
| 18. C2×#14581703 | C22 | semidirect |
| 19. #19127441 | C22 | semidirect |
| 20. #19127441 | C22 | semidirect |
| 177. C83 | #19056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918474 | 2 |
| #24917808 | 2 |
| #24906769 | 2 |
| #24906098 | 2 |
| #24906074 | 2 |
| C83×#3549 | 2 |
| #19056 | 83 |