Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
628 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 85 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. #24913409 | C2 | semidirect |
| 3. #24906176 | C2 | semidirect |
| 4. #24906065 | C2 | semidirect |
| 5. #24905971 | C2 | semidirect |
| 6. #24905355 | C2 | semidirect |
| 7. C83×#3234 | C2 | semidirect |
| 190. #3234 | D83 | semidirect |
| 197. C83 | #10089 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917916 | 2 |
| #24913409 | 2 |
| #24906176 | 2 |
| #24906065 | 2 |
| #24905971 | 2 |
| #24905355 | 2 |
| C83×#3234 | 2 |
| #10089 | 83 |