Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 31. C2×Dic332 | Q8 | semidirect |
| 159. C83 | #13370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918003 | 2 |
| #24909182 | 2 |
| C2×#19127506 | 2 |
| #24908376 | 2 |
| #24905573 | 2 |
| #24905551 | 2 |
| C83×#1382 | 2 |
| #13370 | 83 |