Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
308 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 24. C2×#11719908 | Q8 | semidirect |
| 120. C53 | #13269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276481 | 2 |
| #20276320 | 2 |
| #20272801 | 2 |
| #20272795 | 2 |
| C53×#2961 | 2 |
| #13269 | 53 |