Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
398 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 7. #16811028 | C4 | semidirect |
| 27. #13133151 | Q8 | semidirect |
| 113. C53 | #13275 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811028 | 2 |
| C4×#13133151 | 2 |
| #20272807 | 2 |
| C2×C53×C4⋊C16 | 2 |
| #13275 | 53 |