Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
204 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 63. #11719908 | Q16 | semidirect |
| 119. C53 | #12457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276988 | 2 |
| #20276617 | 2 |
| #20274110 | 2 |
| #20274106 | 2 |
| #20272786 | 2 |
| #20272769 | 2 |
| C53×#1364 | 2 |
| #12457 | 53 |