Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
436 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 11. #19127997 | C4 | semidirect |
| 12. #19127987 | C4 | semidirect |
| 172. C83 | #9304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917270 | 2 |
| #24916543 | 2 |
| #24907475 | 2 |
| #24906026 | 2 |
| #24905867 | 2 |
| #24905358 | 2 |
| C83×#1286 | 2 |
| #9304 | 83 |