Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
358 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 54. C2×Q16×C53 | Q8 | semidirect |
| 176. C53 | #13370 | semidirect |
| 183. C2×Q16 | Dic106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285255 | 2 |
| C2×#16810427 | 2 |
| #20275631 | 2 |
| #20272824 | 2 |
| #20272810 | 2 |
| #20272805 | 2 |
| C53×#2141 | 2 |
| #13370 | 53 |