Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
314 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 21. #16810428 | C4 | semidirect |
| 22. #16810427 | C4 | semidirect |
| 23. #16810426 | C4 | semidirect |
| 24. C53×#358 | C4 | semidirect |
| 172. #358 | #6157 | semidirect |
| 175. C53 | #13154 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811542 | 2 |
| C2×#16811514 | 2 |
| #20290863 | 2 |
| #20290824 | 2 |
| #20289786 | 2 |
| #20289780 | 2 |
| #20276433 | 2 |
| #13154 | 53 |