Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
374 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 99 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. #24908238 | C2 | semidirect |
| 2. #24906239 | C2 | semidirect |
| 3. #24906215 | C2 | semidirect |
| 6. #24905337 | C2 | semidirect |
| 165. C83 | #10603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24908238 | 2 |
| #24906239 | 2 |
| #24906215 | 2 |
| #24906131 | 2 |
| C2×#19127445 | 2 |
| #24905337 | 2 |
| C83×#1965 | 2 |
| #10603 | 83 |