Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
386 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 2. C2×#16811510 | C2 | semidirect |
| 4. #20290819 | C2 | semidirect |
| 5. #20289773 | C2 | semidirect |
| 6. #20289772 | C2 | semidirect |
| 21. #16810425 | C4 | semidirect |
| 22. #16810424 | C4 | semidirect |
| 23. #16810423 | C4 | semidirect |
| 24. C53×#357 | C4 | semidirect |
| 204. #357 | #6157 | semidirect |
| 207. C53 | #13149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811535 | 2 |
| C2×#16811510 | 2 |
| #20290862 | 2 |
| #20290819 | 2 |
| #20289773 | 2 |
| #20289772 | 2 |
| #357×D53 | 2 |
| #13149 | 53 |