Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
438 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 438 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 |
|---|---|---|
| 3. #24905997 | C2 | semidirect |
| 4. #24905828 | C2 | semidirect |
| 5. #24905372 | C2 | semidirect |
| 6. #24905339 | C2 | semidirect |
| 10. #19128034 | C4 | semidirect |
| 11. #19128017 | C4 | semidirect |
| 15. #19127856 | C4 | semidirect |
| 16. #19127839 | C4 | semidirect |
| 224. C83 | #9331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918289 | 2 |
| #24906019 | 2 |
| #24905997 | 2 |
| #24905828 | 2 |
| #24905372 | 2 |
| #24905339 | 2 |
| C83×#2978 | 2 |
| #9331 | 83 |