Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1082 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 179 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. #24918841 | C2 | semidirect |
| 2. #24917889 | C2 | semidirect |
| 3. #24906608 | C2 | semidirect |
| 4. #24906579 | C2 | semidirect |
| 5. #24906546 | C2 | semidirect |
| 6. #24906517 | C2 | semidirect |
| 7. #24906198 | C2 | semidirect |
| 8. #24905914 | C2 | semidirect |
| 9. C83×#3549 | C2 | semidirect |
| 11. #19128251 | C22 | semidirect |
| 13. #19128080 | C22 | semidirect |
| 15. #19128075 | C22 | semidirect |
| 17. #19127991 | C22 | semidirect |
| 20. #19127896 | C22 | semidirect |
| 22. #19127725 | C22 | semidirect |
| 23. C2×C4×C83⋊C8 | C22 | semidirect |
| 24. #19127450 | C22 | semidirect |
| 26. D4⋊(C83⋊C8) | C22 | semidirect |
| 27. D4⋊(C83⋊C8) | C22 | semidirect |
| 206. #3549 | D83 | semidirect |
| 215. C83 | #18686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918841 | 2 |
| #24917889 | 2 |
| #24906608 | 2 |
| #24906579 | 2 |
| #24906546 | 2 |
| #24906517 | 2 |
| #24906198 | 2 |
| #24905914 | 2 |
| C83×#3549 | 2 |
| #18686 | 83 |