Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
426 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 9. #19128097 | C4 | semidirect |
| 10. #19128051 | C4 | semidirect |
| 170. C83 | #9292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918604 | 2 |
| #24916404 | 2 |
| #24908282 | 2 |
| #24906134 | 2 |
| #24905321 | 2 |
| #24905293 | 2 |
| C83×#1518 | 2 |
| #9292 | 83 |