Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 4. #24905343 | C2 | semidirect |
| 5. #24905341 | C2 | semidirect |
| 6. #24905330 | C2 | semidirect |
| 7. C83×#1289 | C2 | semidirect |
| 14. #19127568 | C4 | semidirect |
| 15. #19127563 | C4 | semidirect |
| 18. #19127548 | C4 | semidirect |
| 19. #19127546 | C4 | semidirect |
| 234. #1289 | D83 | semidirect |
| 235. C83 | #8763 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24910405 | 2 |
| #24907448 | 2 |
| #24905779 | 2 |
| #24905343 | 2 |
| #24905341 | 2 |
| #24905330 | 2 |
| C83×#1289 | 2 |
| #8763 | 83 |