Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
528 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 83 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. #24918665 | C2 | semidirect |
| 4. #24906064 | C2 | semidirect |
| 6. #24905319 | C2 | semidirect |
| 7. C83×#1986 | C2 | semidirect |
| 209. #1986 | D83 | semidirect |
| 213. C83 | #10009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918665 | 2 |
| #24917558 | 2 |
| #24912624 | 2 |
| #24906064 | 2 |
| #24905907 | 2 |
| #24905319 | 2 |
| C83×#1986 | 2 |
| #10009 | 83 |