Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
316 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 89 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. #24909258 | C2 | semidirect |
| 2. #24909228 | C2 | semidirect |
| 5. #24908251 | C2 | semidirect |
| 6. #24905566 | C2 | semidirect |
| 138. C83 | #13472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909258 | 2 |
| #24909228 | 2 |
| C2×#19127514 | 2 |
| #24908374 | 2 |
| #24908251 | 2 |
| #24905566 | 2 |
| C2×#361×C83 | 2 |
| #13472 | 83 |