Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
390 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 95 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. #24916558 | C2 | semidirect |
| 5. #24905333 | C2 | semidirect |
| 6. #24905326 | C2 | semidirect |
| 7. C83×#1552 | C2 | semidirect |
| 162. #1552 | 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 |
|---|---|
| #24918661 | 2 |
| #24916558 | 2 |
| #24906097 | 2 |
| #24905861 | 2 |
| #24905333 | 2 |
| #24905326 | 2 |
| C83×#1552 | 2 |
| #9372 | 83 |