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. #24920037 | C2 | semidirect |
| 2. #24909704 | C2 | semidirect |
| 3. #24909500 | C2 | semidirect |
| 4. #24905516 | C2 | semidirect |
| 5. #24905432 | C2 | semidirect |
| 6. #24905421 | C2 | semidirect |
| 154. C83 | #12349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920037 | 2 |
| #24909704 | 2 |
| #24909500 | 2 |
| #24905516 | 2 |
| #24905432 | 2 |
| #24905421 | 2 |
| C83×#1687 | 2 |
| #12349 | 83 |