Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
424 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 111. C2×#88322 | Q16 | semidirect |
| 195. C53 | #9048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284754 | 2 |
| #20283652 | 2 |
| #20275656 | 2 |
| #20273370 | 2 |
| #20272610 | 2 |
| #20272559 | 2 |
| C53×#1487 | 2 |
| #9048 | 53 |