Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
470 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 131 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. #24920566 | C2 | semidirect |
| 2. #24909199 | C2 | semidirect |
| 3. #24907509 | C2 | semidirect |
| 4. #24905570 | C2 | semidirect |
| 16. #470×C83 | C4 | semidirect |
| 17. #469×C83 | C4 | semidirect |
| 24. #14581732 | D4 | semidirect |
| 144. C83 | #13077 | semidirect |
| 151. #470 | Dic83 | semidirect |
| 152. #469 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920566 | 2 |
| #24909199 | 2 |
| #24907509 | 2 |
| #24905570 | 2 |
| C83×#3060 | 2 |
| #13077 | 83 |