Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
158 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 18. #13133123 | Q8 | semidirect |
| 21. C32×C53 | Q8 | semidirect |
| 64. C53 | #13731 | semidirect |
| 73. C32 | Dic106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276989 | 2 |
| #20272915 | 2 |
| #20272914 | 2 |
| C32×Dic53 | 2 |
| C53×#1423 | 2 |
| #13731 | 53 |