Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
542 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 119 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. #24910649 | C2 | semidirect |
| 3. C2×#19127443 | C2 | semidirect |
| 4. #24905345 | C2 | semidirect |
| 17. #490×C83 | C4 | semidirect |
| 141. C83 | #9002 | semidirect |
| 145. #490 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24910649 | 2 |
| #24908288 | 2 |
| C2×#19127443 | 2 |
| #24905345 | 2 |
| C2×#490×C83 | 2 |
| #9002 | 83 |