Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
710 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 132 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. #20290843 | C2 | semidirect |
| 2. #20290650 | C2 | semidirect |
| 3. #20289909 | C2 | semidirect |
| 12. #16811000 | C4 | semidirect |
| 13. #16810999 | C4 | semidirect |
| 16. C53×#493 | C4 | semidirect |
| 91. C8×C53 | #102 | semidirect |
| 92. #88322 | #102 | semidirect |
| 125. #493 | #6157 | semidirect |
| 132. C53 | #9837 | semidirect |
| 208. C8 | #13133279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290843 | 2 |
| #20290650 | 2 |
| #20289909 | 2 |
| #493×D53 | 2 |
| #9837 | 53 |