Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
348 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 70 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. #20291086 | C2 | semidirect |
| 2. #20289935 | C2 | semidirect |
| 3. #20289680 | C2 | semidirect |
| 4. #20289679 | C2 | semidirect |
| 5. #20289678 | C2 | semidirect |
| 6. #20289677 | C2 | semidirect |
| 9. #16811545 | C22 | semidirect |
| 10. #16811545 | C22 | semidirect |
| 14. #16811464 | C22 | semidirect |
| 15. C8×#88324 | C22 | semidirect |
| 192. C53 | #11670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291086 | 2 |
| #20289935 | 2 |
| #20289680 | 2 |
| #20289679 | 2 |
| #20289678 | 2 |
| #20289677 | 2 |
| #20283623 | 2 |
| #11670 | 53 |