Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
690 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 1. #20276404 | C2 | semidirect |
| 2. C2×#16810420 | C2 | semidirect |
| 3. #20274829 | C2 | semidirect |
| 191. C53 | #12729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276404 | 2 |
| C2×#16810420 | 2 |
| #20274829 | 2 |
| C53×#3510 | 2 |
| #12729 | 53 |