Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
200 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 200 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 |
|---|---|---|
| 45. C16×C53 | Q16 | semidirect |
| 89. C53 | #12460 | semidirect |
| 119. C16 | #11719925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276623 | 2 |
| #20274106 | 2 |
| #20272789 | 2 |
| #20272770 | 2 |
| C53×#2252 | 2 |
| #12460 | 53 |