Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
396 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 396 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. #24909026 | C2 | semidirect |
| 2. #24909001 | C2 | semidirect |
| 4. #24905289 | C2 | semidirect |
| 5. #24905286 | C2 | semidirect |
| 194. C83 | #7834 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909026 | 2 |
| #24909001 | 2 |
| #24908996 | 2 |
| #24905289 | 2 |
| #24905286 | 2 |
| #24905284 | 2 |
| C83×#2808 | 2 |
| #7834 | 83 |