Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 48. Q16×C53 | Q16 | semidirect |
| 120. C53 | #12448 | semidirect |
| 147. Q16 | #11719925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276867 | 2 |
| #20274332 | 2 |
| Q16×#88322 | 2 |
| #20272784 | 2 |
| #20272773 | 2 |
| #20272772 | 2 |
| C53×#2227 | 2 |
| #12448 | 53 |