Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
422 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 9. #19128104 | C4 | semidirect |
| 10. #19128080 | C4 | semidirect |
| 11. #19128053 | C4 | semidirect |
| 12. #19128051 | C4 | semidirect |
| 101. C42×C83 | Q16 | semidirect |
| 161. C83 | #9848 | semidirect |
| 255. C42 | #13050580 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918045 | 2 |
| #24908440 | 2 |
| #24907209 | 2 |
| #24906221 | 2 |
| #24905918 | 2 |
| #24905917 | 2 |
| C83×#1994 | 2 |
| #9848 | 83 |