Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
416 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 95 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. #24916558 | C2 | semidirect |
| 5. #24905324 | C2 | semidirect |
| 6. #24905292 | C2 | semidirect |
| 7. C83×#1506 | C2 | semidirect |
| 9. #19128080 | C4 | semidirect |
| 10. #19128075 | C4 | semidirect |
| 11. #19128053 | C4 | semidirect |
| 12. #19128049 | C4 | semidirect |
| 170. #1506 | D83 | semidirect |
| 175. C83 | #9282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918415 | 2 |
| #24916558 | 2 |
| #24905970 | 2 |
| #24905931 | 2 |
| #24905324 | 2 |
| #24905292 | 2 |
| C83×#1506 | 2 |
| #9282 | 83 |