Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
158 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 28. #13133123 | Q8 | semidirect |
| 94. C53 | #13660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×Dic106 | 2 |
| #20272910 | 2 |
| #20272849 | 2 |
| #20272848 | 2 |
| C32×Dic53 | 2 |
| C53×C4⋊C32 | 2 |
| #13660 | 53 |