Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
996 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 996 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. #24918850 | C2 | semidirect |
| 2. #24917785 | C2 | semidirect |
| 3. #24906691 | C2 | semidirect |
| 4. #24906642 | C2 | semidirect |
| 5. #24906198 | C2 | semidirect |
| 6. #24905914 | C2 | semidirect |
| 8. #19128258 | C22 | semidirect |
| 10. #19128051 | C22 | semidirect |
| 13. #19127981 | C22 | semidirect |
| 15. #19127906 | C22 | semidirect |
| 17. #19127725 | C22 | semidirect |
| 19. C2×C4×C83⋊C8 | C22 | semidirect |
| 20. #19127450 | C22 | semidirect |
| 22. D4⋊(C83⋊C8) | C22 | semidirect |
| 187. C83 | #18691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918850 | 2 |
| #24917785 | 2 |
| #24906691 | 2 |
| #24906642 | 2 |
| #24906198 | 2 |
| #24905914 | 2 |
| C83×#3549 | 2 |
| #18691 | 83 |