Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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. #24908186 | C2 | semidirect |
| 2. #24906120 | C2 | semidirect |
| 4. #24905962 | C2 | semidirect |
| 6. #24905294 | C2 | semidirect |
| 196. C83 | #10547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24908186 | 2 |
| #24906120 | 2 |
| #24906112 | 2 |
| #24905962 | 2 |
| #24905958 | 2 |
| #24905294 | 2 |
| C83×#3135 | 2 |
| #10547 | 83 |