Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
314 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 91 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. #24909236 | C2 | semidirect |
| 5. #24908211 | C2 | semidirect |
| 6. #24905575 | C2 | semidirect |
| 7. C83×#2150 | C2 | semidirect |
| 143. #2150 | D83 | semidirect |
| 149. C83 | #13466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909236 | 2 |
| #24909200 | 2 |
| #24909192 | 2 |
| #24908351 | 2 |
| #24908211 | 2 |
| #24905575 | 2 |
| C83×#2150 | 2 |
| #13466 | 83 |