Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
514 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 99 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. #24916593 | C2 | semidirect |
| 3. C4×#14581720 | C2 | semidirect |
| 4. #24905880 | C2 | semidirect |
| 5. #24905352 | C2 | semidirect |
| 6. #24905296 | C2 | semidirect |
| 7. C83×#1962 | C2 | semidirect |
| 10. #19127993 | C4 | semidirect |
| 11. #19127988 | C4 | semidirect |
| 12. #19127898 | C4 | semidirect |
| 13. #19127893 | C4 | semidirect |
| 179. Dic166 | #104 | semidirect |
| 219. #1962 | D83 | semidirect |
| 224. C83 | #8970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917517 | 2 |
| #24916593 | 2 |
| C4×#14581720 | 2 |
| #24905880 | 2 |
| #24905352 | 2 |
| #24905296 | 2 |
| C83×#1962 | 2 |
| #8970 | 83 |