Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
516 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 119 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×#16810436 | C2 | semidirect |
| 3. #20276430 | C2 | semidirect |
| 4. #20275625 | C2 | semidirect |
| 5. #20272810 | C2 | semidirect |
| 6. #20272804 | C2 | semidirect |
| 7. C53×#2948 | C2 | semidirect |
| 11. C2×#13133158 | C4 | semidirect |
| 32. C2×D424 | C2×C4 | semidirect |
| 40. C2×#11719908 | C2×C4 | semidirect |
| 161. #2948 | D53 | semidirect |
| 191. C53 | #13017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133158 | 2 |
| C2×#16810436 | 2 |
| #20276430 | 2 |
| #20275625 | 2 |
| #20272810 | 2 |
| #20272804 | 2 |
| C53×#2948 | 2 |
| #13017 | 53 |