Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
642 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 236 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. #20291684 | C2 | semidirect |
| 2. #20291107 | C2 | semidirect |
| 3. #20291104 | C2 | semidirect |
| 4. #20291056 | C2 | semidirect |
| 5. C2×#16811522 | C2 | semidirect |
| 6. #20290926 | C2 | semidirect |
| 9. #16811682 | C22 | semidirect |
| 14. #16811545 | C22 | semidirect |
| 15. #16811522 | C22 | semidirect |
| 16. #16811522 | C22 | semidirect |
| 17. #16811512 | C22 | semidirect |
| 18. #16811509 | C22 | semidirect |
| 147. C53 | #33442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291684 | 2 |
| #20291107 | 2 |
| #20291104 | 2 |
| #20291056 | 2 |
| C2×#16811522 | 2 |
| #20290926 | 2 |
| #20283617 | 2 |
| #33442 | 53 |