Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
416 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #24905937 | C2 | semidirect |
| 5. #24905935 | C2 | semidirect |
| 6. #24905362 | C2 | semidirect |
| 7. C83×#1302 | C2 | semidirect |
| 159. #1302 | D83 | semidirect |
| 160. C83 | #9005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917809 | 2 |
| #24916533 | 2 |
| #24906123 | 2 |
| #24905937 | 2 |
| #24905935 | 2 |
| #24905362 | 2 |
| C83×#1302 | 2 |
| #9005 | 83 |