Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
312 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 91 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. #24906251 | C2 | semidirect |
| 5. #24905354 | C2 | semidirect |
| 6. #24905300 | C2 | semidirect |
| 7. C83×#1450 | C2 | semidirect |
| 153. #1450 | D83 | semidirect |
| 156. C83 | #9586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24906251 | 2 |
| #24906123 | 2 |
| #24905915 | 2 |
| #24905879 | 2 |
| #24905354 | 2 |
| #24905300 | 2 |
| C83×#1450 | 2 |
| #9586 | 83 |