Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
516 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20283567 | C2 | semidirect |
| 3. #20276432 | C2 | semidirect |
| 4. #20275623 | C2 | semidirect |
| 5. #20272812 | C2 | semidirect |
| 6. #20272805 | C2 | semidirect |
| 7. C2×C53×#361 | C2 | semidirect |
| 12. C2×#13133158 | C4 | semidirect |
| 32. C2×D424 | C2×C4 | semidirect |
| 42. C2×#11719908 | C2×C4 | semidirect |
| 162. C2×#361 | 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 |
| #20283567 | 2 |
| #20276432 | 2 |
| #20275623 | 2 |
| #20272812 | 2 |
| #20272805 | 2 |
| C2×C53×#361 | 2 |
| #13017 | 53 |