Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
400 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 400 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 |
|---|---|---|
| 33. #14581792 | Q8 | semidirect |
| 188. C83 | #10359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24915735 | 2 |
| #24908436 | 2 |
| #24908435 | 2 |
| #24908283 | 2 |
| #24905345 | 2 |
| C83×#1295 | 2 |
| #10359 | 83 |