Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
632 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 632 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 |
|---|---|---|
| 1. #24910644 | C2 | semidirect |
| 2. C2×#19127500 | C2 | semidirect |
| 4. #24905589 | C2 | semidirect |
| 19. #456×C83 | C4 | semidirect |
| 180. C83 | #13056 | semidirect |
| 185. #456 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24910644 | 2 |
| C2×#19127500 | 2 |
| #24907422 | 2 |
| #24905589 | 2 |
| C2×#456×C83 | 2 |
| #13056 | 83 |