Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
418 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 71 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. #24909157 | C2 | semidirect |
| 4. #24908015 | C2 | semidirect |
| 6. #24905586 | C2 | semidirect |
| 7. C83×#1858 | C2 | semidirect |
| 198. #1858 | D83 | semidirect |
| 200. C83 | #13430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918336 | 2 |
| #24909157 | 2 |
| #24909154 | 2 |
| #24908015 | 2 |
| #24908010 | 2 |
| #24905586 | 2 |
| C83×#1858 | 2 |
| #13430 | 83 |