Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
424 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 107. #11719940 | Q16 | semidirect |
| 244. C53 | #9268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291512 | 2 |
| #20290907 | 2 |
| #20290233 | 2 |
| C2×#16811483 | 2 |
| #20289606 | 2 |
| #20289559 | 2 |
| #20285661 | 2 |
| #9268 | 53 |