Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
326 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 15. #19127450 | C4 | semidirect |
| 16. #19127447 | C4 | semidirect |
| 146. C83 | #9584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24907316 | 2 |
| #24906239 | 2 |
| #24906120 | 2 |
| #24905866 | 2 |
| #24905358 | 2 |
| #24905296 | 2 |
| C83×#1994 | 2 |
| #9584 | 83 |