Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
212 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 52. #11719925 | C16 | semidirect |
| 120. C53 | #12059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11719908 | 2 |
| #20276617 | 2 |
| C8×#11719925 | 2 |
| #20272778 | 2 |
| #20272695 | 2 |
| #20272634 | 2 |
| C53×Q8⋊C16 | 2 |
| #12059 | 53 |