Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
776 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 776 conjugacy classes of subgroups — too many to draw. Only its 107 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. #24907451 | C2 | semidirect |
| 2. #24905784 | C2 | semidirect |
| 3. #24905460 | C2 | semidirect |
| 8. #19127468 | C22 | semidirect |
| 10. #19127425 | C22 | semidirect |
| 11. C23×D4×C83 | C4 | semidirect |
| 15. #394×C83 | C4 | semidirect |
| 18. #380×C83 | C4 | semidirect |
| 206. C83 | #11873 | semidirect |
| 207. C23×D4 | Dic83 | semidirect |
| 213. #394 | Dic83 | semidirect |
| 217. #380 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24907451 | 2 |
| #24905784 | 2 |
| #24905460 | 2 |
| C83×#2408 | 2 |
| #11873 | 83 |