Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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. #24909059 | C2 | semidirect |
| 5. #24908254 | C2 | semidirect |
| 6. #24905579 | C2 | semidirect |
| 7. C83×#1382 | C2 | semidirect |
| 15. #19127516 | C4 | semidirect |
| 16. #19127513 | C4 | semidirect |
| 147. #1382 | D83 | semidirect |
| 148. C83 | #13146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909210 | 2 |
| C2×#19127509 | 2 |
| #24909059 | 2 |
| #24908359 | 2 |
| #24908254 | 2 |
| #24905579 | 2 |
| C83×#1382 | 2 |
| #13146 | 83 |