Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 89 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. #24916560 | C2 | semidirect |
| 3. #24906161 | C2 | semidirect |
| 6. #24905324 | C2 | semidirect |
| 7. C83×#1290 | C2 | semidirect |
| 165. #1290 | D83 | semidirect |
| 167. C83 | #9372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918663 | 2 |
| #24916560 | 2 |
| #24906161 | 2 |
| #24906097 | 2 |
| #24905861 | 2 |
| #24905324 | 2 |
| C83×#1290 | 2 |
| #9372 | 83 |