Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
458 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 105 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. #24906149 | C2 | semidirect |
| 4. #24906147 | C2 | semidirect |
| 6. #24905321 | C2 | semidirect |
| 7. C83×#1286 | C2 | semidirect |
| 194. #1286 | D83 | semidirect |
| 195. C83 | #9194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916100 | 2 |
| #24913287 | 2 |
| #24906149 | 2 |
| #24906147 | 2 |
| #24905775 | 2 |
| #24905321 | 2 |
| C83×#1286 | 2 |
| #9194 | 83 |