Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
450 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 144. Q8×C53 | #101 | semidirect |
| 239. C53 | #9252 | semidirect |
| 355. Q8 | #13133278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11719940 | 2 |
| #20290858 | 2 |
| #20290224 | 2 |
| #20290043 | 2 |
| #20289585 | 2 |
| #20289560 | 2 |
| C2×#16810906 | 2 |
| #9252 | 53 |