Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
530 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #24905341 | C2 | semidirect |
| 4. #24905330 | C2 | semidirect |
| 11. #19127567 | C4 | semidirect |
| 12. #19127561 | C4 | semidirect |
| 14. C4×C4⋊Dic83 | C4 | semidirect |
| 15. C2×C83⋊#95 | C4 | semidirect |
| 195. C83 | #8760 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24910373 | 2 |
| #24905781 | 2 |
| #24905341 | 2 |
| #24905330 | 2 |
| C83×#1799 | 2 |
| #8760 | 83 |