Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
344 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20276384 | C2 | semidirect |
| 3. #20272891 | C2 | semidirect |
| 4. #20272873 | C2 | semidirect |
| 5. C53×#2134 | C2 | semidirect |
| 6. #16811228 | C4 | semidirect |
| 8. #16810999 | C4 | semidirect |
| 9. #16810987 | C4 | semidirect |
| 15. #16810684 | C4 | semidirect |
| 27. #13133214 | C2×C4 | semidirect |
| 28. #13133209 | C2×C4 | semidirect |
| 42. #13133128 | C2×C4 | semidirect |
| 43. C4×#88322 | C2×C4 | semidirect |
| 153. #2134 | D53 | semidirect |
| 181. C53 | #13605 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285765 | 2 |
| #20276384 | 2 |
| #20272891 | 2 |
| #20272873 | 2 |
| C53×#2134 | 2 |
| #13605 | 53 |