Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
476 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #24908440 | C2 | semidirect |
| 5. #24905883 | C2 | semidirect |
| 6. #24905354 | C2 | semidirect |
| 7. C83×#1276 | C2 | semidirect |
| 11. #19127987 | C4 | semidirect |
| 12. #19127982 | C4 | semidirect |
| 13. #19127912 | C4 | semidirect |
| 14. #19127907 | C4 | semidirect |
| 212. #1276 | D83 | semidirect |
| 213. C83 | #8972 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917535 | 2 |
| #24916592 | 2 |
| #24908440 | 2 |
| C4×#14581720 | 2 |
| #24905883 | 2 |
| #24905354 | 2 |
| C83×#1276 | 2 |
| #8972 | 83 |