Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
452 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 91 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. #24906057 | C2 | semidirect |
| 5. #24905974 | C2 | semidirect |
| 6. #24905334 | C2 | semidirect |
| 7. C83×#1300 | C2 | semidirect |
| 11. #19127997 | C4 | semidirect |
| 12. #19127992 | C4 | semidirect |
| 13. #19127912 | C4 | semidirect |
| 14. #19127907 | C4 | semidirect |
| 200. #1300 | D83 | semidirect |
| 202. C83 | #9159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917626 | 2 |
| #24916478 | 2 |
| #24907274 | 2 |
| #24906057 | 2 |
| #24905974 | 2 |
| #24905334 | 2 |
| C83×#1300 | 2 |
| #9159 | 83 |