Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
302 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 1. #24909646 | C2 | semidirect |
| 2. #24909641 | C2 | semidirect |
| 3. #24908968 | C2 | semidirect |
| 4. #24905478 | C2 | semidirect |
| 5. #24905478 | C2 | semidirect |
| 6. #24905405 | C2 | semidirect |
| 156. C83 | #12294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909646 | 2 |
| #24909641 | 2 |
| #24908968 | 2 |
| #24905478 | 2 |
| #24905405 | 2 |
| C83×#3259 | 2 |
| #12294 | 83 |