Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
158 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 16. #13133123 | Q8 | semidirect |
| 67. C53 | #13731 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276990 | 2 |
| #20272914 | 2 |
| C4×#13133123 | 2 |
| C53×#2252 | 2 |
| #13731 | 53 |