Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1004 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 163 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. #20289129 | C2 | semidirect |
| 2. #20285656 | C2 | semidirect |
| 3. #20273791 | C2 | semidirect |
| 4. #20273772 | C2 | semidirect |
| 5. #20273377 | C2 | semidirect |
| 6. #20273137 | C2 | semidirect |
| 9. #16811359 | C22 | semidirect |
| 10. #16811353 | C22 | semidirect |
| 21. #16810372 | C22 | semidirect |
| 22. #16810367 | C22 | semidirect |
| 23. #16810355 | C22 | semidirect |
| 198. C53 | #18718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289129 | 2 |
| #20285656 | 2 |
| #20273791 | 2 |
| #20273772 | 2 |
| #20273377 | 2 |
| #20273137 | 2 |
| C53×#3151 | 2 |
| #18718 | 53 |