Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
396 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 91 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. #24907509 | C2 | semidirect |
| 3. #24905449 | C2 | semidirect |
| 4. C83×#2115 | C2 | semidirect |
| 5. C22×D664 | C4 | semidirect |
| 7. #19127954 | C4 | semidirect |
| 12. #19127739 | C4 | semidirect |
| 15. #19127458 | C22 | semidirect |
| 19. #349×C83 | C22 | semidirect |
| 152. #2115 | D83 | semidirect |
| 155. C83 | #11868 | semidirect |
| 169. #349 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917111 | 2 |
| #24907509 | 2 |
| #24905449 | 2 |
| C83×#2115 | 2 |
| #11868 | 83 |