Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
564 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 131 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. #24916374 | C2 | semidirect |
| 2. #24909675 | C2 | semidirect |
| 3. #24909631 | C2 | semidirect |
| 4. #24909536 | C2 | semidirect |
| 5. #24909408 | C2 | semidirect |
| 6. #24909359 | C2 | semidirect |
| 7. #24909275 | C2 | semidirect |
| 8. C83×#3184 | C2 | semidirect |
| 18. #19127523 | C22 | semidirect |
| 19. #19127522 | C22 | semidirect |
| 20. #19127514 | C22 | semidirect |
| 23. #19127479 | C22 | semidirect |
| 25. #498×C83 | C22 | semidirect |
| 26. #493×C83 | C22 | semidirect |
| 31. #442×C83 | C22 | semidirect |
| 80. Dic332 | #41 | semidirect |
| 84. D664 | #41 | semidirect |
| 170. #3184 | D83 | semidirect |
| 178. C83 | #33688 | semidirect |
| 183. #498 | C2×D83 | semidirect |
| 184. #493 | C2×D83 | semidirect |
| 193. #442 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916374 | 2 |
| #24909675 | 2 |
| #24909631 | 2 |
| #24909536 | 2 |
| #24909408 | 2 |
| #24909359 | 2 |
| #24909275 | 2 |
| C83×#3184 | 2 |
| #33688 | 83 |