Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
314 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 314 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 |
|---|---|---|
| 1. #24909235 | C2 | semidirect |
| 5. #24905566 | C2 | semidirect |
| 6. #24905547 | C2 | semidirect |
| 7. C83×#1773 | C2 | semidirect |
| 15. #19127516 | C4 | semidirect |
| 16. #19127513 | C4 | semidirect |
| 143. #1773 | D83 | semidirect |
| 146. C83 | #13140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909235 | 2 |
| #24909210 | 2 |
| #24909198 | 2 |
| #24908356 | 2 |
| #24905566 | 2 |
| #24905547 | 2 |
| C83×#1773 | 2 |
| #13140 | 83 |