Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
558 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 99. C2×C4×C53 | Q32 | semidirect |
| 154. C53 | #13330 | semidirect |
| 241. C2×C4 | #13133163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133163 | 2 |
| C2×#16811003 | 2 |
| C2×#16810426 | 2 |
| #20272793 | 2 |
| C53×#1969 | 2 |
| #13330 | 53 |