Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1312 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1312 conjugacy classes of subgroups — too many to draw. Only its 271 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. #24915942 | C2 | semidirect |
| 3. #24909154 | C2 | semidirect |
| 4. #24909146 | C2 | semidirect |
| 5. C83×#2888 | C2 | semidirect |
| 17. #19127685 | C22 | semidirect |
| 19. #19127499 | C22 | semidirect |
| 20. #19127497 | C22 | semidirect |
| 23. #413×C83 | C22 | semidirect |
| 187. #2888 | D83 | semidirect |
| 190. C83 | #33373 | semidirect |
| 205. #413 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24921237 | 2 |
| #24915942 | 2 |
| #24909154 | 2 |
| #24909146 | 2 |
| C83×#2888 | 2 |
| #33373 | 83 |