Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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. #24909671 | C2 | semidirect |
| 3. #24909654 | C2 | semidirect |
| 4. #24909249 | C2 | semidirect |
| 5. #24909173 | C2 | semidirect |
| 6. #24909074 | C2 | semidirect |
| 7. C2×#427×C83 | C2 | semidirect |
| 16. #19127528 | C22 | semidirect |
| 17. #19127526 | C22 | semidirect |
| 18. #19127504 | C22 | semidirect |
| 19. #19127501 | C22 | semidirect |
| 145. C2×#427 | D83 | semidirect |
| 151. C83 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917044 | 2 |
| #24909671 | 2 |
| #24909654 | 2 |
| #24909249 | 2 |
| #24909173 | 2 |
| #24909074 | 2 |
| C2×#427×C83 | 2 |
| #33647 | 83 |