Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
502 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 81 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. #24918851 | C2 | semidirect |
| 2. #24918663 | C2 | semidirect |
| 4. #24908294 | C2 | semidirect |
| 5. #24905976 | C2 | semidirect |
| 6. #24905972 | C2 | semidirect |
| 7. C83×#1307 | C2 | semidirect |
| 209. #1307 | D83 | semidirect |
| 210. C83 | #10214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918851 | 2 |
| #24918663 | 2 |
| #24918460 | 2 |
| #24908294 | 2 |
| #24905976 | 2 |
| #24905972 | 2 |
| C83×#1307 | 2 |
| #10214 | 83 |