Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
458 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 71 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. #24909128 | C2 | semidirect |
| 3. #24905625 | C2 | semidirect |
| 4. C83×#2126 | C2 | semidirect |
| 7. C2×#14581789 | C4 | semidirect |
| 11. #19128075 | C4 | semidirect |
| 13. C4×#13050574 | C4 | semidirect |
| 15. #19127494 | C22 | semidirect |
| 19. #353×C83 | C22 | semidirect |
| 160. #2126 | D83 | semidirect |
| 162. C83 | #13585 | semidirect |
| 177. #353 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917916 | 2 |
| #24909128 | 2 |
| #24905625 | 2 |
| C83×#2126 | 2 |
| #13585 | 83 |