Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
382 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. C2×#16810440 | C2 | semidirect |
| 3. C2×#16810438 | C2 | semidirect |
| 6. #20272828 | C2 | semidirect |
| 7. C53×#2161 | C2 | semidirect |
| 155. #2161 | D53 | semidirect |
| 183. C53 | #13390 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810899 | 2 |
| C2×#16810440 | 2 |
| C2×#16810438 | 2 |
| #20276344 | 2 |
| #20274762 | 2 |
| #20272828 | 2 |
| C53×#2161 | 2 |
| #13390 | 53 |