Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
384 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 180. C83 | #8775 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24910429 | 2 |
| C4×#14581710 | 2 |
| #24905806 | 2 |
| #24905356 | 2 |
| #24905329 | 2 |
| #24905328 | 2 |
| C83×#1300 | 2 |
| #8775 | 83 |