Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
428 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #24916560 | C2 | semidirect |
| 3. #24906191 | C2 | semidirect |
| 6. #24905326 | C2 | semidirect |
| 7. C83×#1307 | C2 | semidirect |
| 174. #1307 | D83 | semidirect |
| 176. C83 | #9530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917563 | 2 |
| #24916560 | 2 |
| #24906191 | 2 |
| #24905887 | 2 |
| #24905803 | 2 |
| #24905326 | 2 |
| C83×#1307 | 2 |
| #9530 | 83 |