Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
472 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 167 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 |
|---|---|---|
| 73. Q8×C53 | Q32 | semidirect |
| 122. C53 | #33930 | semidirect |
| 174. Q8 | #13133163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287721 | 2 |
| #20276944 | 2 |
| #20276864 | 2 |
| #20276765 | 2 |
| Q8×#11719908 | 2 |
| C4×#13133163 | 2 |
| Q8×Q16×C53 | 2 |
| #33930 | 53 |