Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
512 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 99 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. #24918614 | C2 | semidirect |
| 4. #24908406 | C2 | semidirect |
| 6. #24905313 | C2 | semidirect |
| 7. C83×#1981 | C2 | semidirect |
| 194. #1981 | D83 | semidirect |
| 197. C83 | #10202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918780 | 2 |
| #24918614 | 2 |
| #24917859 | 2 |
| #24908406 | 2 |
| #24905957 | 2 |
| #24905313 | 2 |
| C83×#1981 | 2 |
| #10202 | 83 |