Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
412 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 127 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. #24909229 | C2 | semidirect |
| 4. #24907587 | C2 | semidirect |
| 5. #24905579 | C2 | semidirect |
| 6. #24905564 | C2 | semidirect |
| 19. #442×C83 | C4 | semidirect |
| 145. C83 | #12826 | semidirect |
| 150. #442 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909229 | 2 |
| C2×#19127514 | 2 |
| #24909179 | 2 |
| #24907587 | 2 |
| #24905579 | 2 |
| #24905564 | 2 |
| C83×#2948 | 2 |
| #12826 | 83 |