Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
282 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 56. Dic332 | Q16 | semidirect |
| 125. C83 | #12406 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic332 | 2 |
| #24909743 | 2 |
| #24909602 | 2 |
| #24905522 | 2 |
| Q8⋊(C83⋊C16) | 2 |
| #24905426 | 2 |
| C83×#1674 | 2 |
| #12406 | 83 |