Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
164 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 19. Dic664 | Q8 | semidirect |
| 72. C83 | #13704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909738 | 2 |
| C4×Dic664 | 2 |
| #24905665 | 2 |
| #24905645 | 2 |
| C83×C4⋊C32 | 2 |
| #13704 | 83 |