Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
206 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 64. #11719910 | Q16 | semidirect |
| 120. C53 | #12053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291130 | 2 |
| Q8×#11719910 | 2 |
| #20289744 | 2 |
| Q8⋊#11719910 | 2 |
| #20289627 | 2 |
| Q16×#88322 | 2 |
| #12053 | 53 |