Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
450 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. C2×#19127517 | C2 | semidirect |
| 5. #24905579 | C2 | semidirect |
| 6. #24905567 | C2 | semidirect |
| 7. C83×#2141 | C2 | semidirect |
| 15. #19127973 | C4 | semidirect |
| 165. #2141 | D83 | semidirect |
| 169. C83 | #13069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920565 | 2 |
| C2×#19127973 | 2 |
| C2×#19127517 | 2 |
| #24907514 | 2 |
| #24905579 | 2 |
| #24905567 | 2 |
| C83×#2141 | 2 |
| #13069 | 83 |