Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
442 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 72 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. #20291600 | C2 | semidirect |
| 2. #20290204 | C2 | semidirect |
| 3. #20290135 | C2 | semidirect |
| 4. #20290135 | C2 | semidirect |
| 5. #20289582 | C2 | semidirect |
| 6. #20289575 | C2 | semidirect |
| 20. #16811021 | C4 | semidirect |
| 21. #16810969 | C4 | semidirect |
| 22. #16810969 | C4 | semidirect |
| 26. C53×#493 | C4 | semidirect |
| 178. #493 | #6157 | semidirect |
| 194. C53 | #9417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291600 | 2 |
| #20290204 | 2 |
| #20290135 | 2 |
| #20289582 | 2 |
| #20289575 | 2 |
| #20285451 | 2 |
| #9417 | 53 |