Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
378 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. #24909223 | C2 | semidirect |
| 5. #24907586 | C2 | semidirect |
| 6. #24905556 | C2 | semidirect |
| 7. C83×#1389 | C2 | semidirect |
| 11. #19127822 | C4 | semidirect |
| 148. #1389 | D83 | semidirect |
| 150. C83 | #12829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916379 | 2 |
| #24909223 | 2 |
| #24909213 | 2 |
| #24909168 | 2 |
| #24907586 | 2 |
| #24905556 | 2 |
| C83×#1389 | 2 |
| #12829 | 83 |