Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 2. #24909680 | C2 | semidirect |
| 3. #24909636 | C2 | semidirect |
| 4. #24909541 | C2 | semidirect |
| 6. #24909352 | C2 | semidirect |
| 7. #24909279 | C2 | semidirect |
| 8. C83×#3177 | C2 | semidirect |
| 18. #19127523 | C22 | semidirect |
| 19. #19127522 | C22 | semidirect |
| 20. #19127517 | C22 | semidirect |
| 23. #19127479 | C22 | semidirect |
| 25. #499×C83 | C22 | semidirect |
| 26. #494×C83 | C22 | semidirect |
| 30. #441×C83 | C22 | semidirect |
| 161. #3177 | D83 | semidirect |
| 169. C83 | #33693 | semidirect |
| 174. #499 | C2×D83 | semidirect |
| 175. #494 | C2×D83 | semidirect |
| 183. #441 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916367 | 2 |
| #24909680 | 2 |
| #24909636 | 2 |
| #24909541 | 2 |
| #24909413 | 2 |
| #24909352 | 2 |
| #24909279 | 2 |
| C83×#3177 | 2 |
| #33693 | 83 |