Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
530 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 1. #20291198 | C2 | semidirect |
| 2. #20290879 | C2 | semidirect |
| 3. #20290104 | C2 | semidirect |
| 4. #20290055 | C2 | semidirect |
| 5. #20289602 | C2 | semidirect |
| 6. #20289567 | C2 | semidirect |
| 25. #16810914 | C4 | semidirect |
| 26. #16810913 | C4 | semidirect |
| 27. #16810815 | C4 | semidirect |
| 32. C53×#459 | C4 | semidirect |
| 243. #459 | #6157 | semidirect |
| 262. C53 | #9329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291198 | 2 |
| #20290879 | 2 |
| #20290104 | 2 |
| #20290055 | 2 |
| #20289602 | 2 |
| #20289567 | 2 |
| #20284805 | 2 |
| #9329 | 53 |