Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
424 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 83 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. #24906200 | C2 | semidirect |
| 5. #24905883 | C2 | semidirect |
| 6. #24905354 | C2 | semidirect |
| 7. C83×#1574 | C2 | semidirect |
| 167. #1574 | D83 | semidirect |
| 172. C83 | #10492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918406 | 2 |
| #24908302 | 2 |
| #24906200 | 2 |
| #24906130 | 2 |
| #24905883 | 2 |
| #24905354 | 2 |
| C83×#1574 | 2 |
| #10492 | 83 |