Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
494 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 79 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. #24909148 | C2 | semidirect |
| 2. #24906055 | C2 | semidirect |
| 3. #24905611 | C2 | semidirect |
| 8. #19127498 | C22 | semidirect |
| 10. #19127441 | C22 | semidirect |
| 178. C83 | #13564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909148 | 2 |
| #24906055 | 2 |
| #24905611 | 2 |
| C83×#3018 | 2 |
| #13564 | 83 |