Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
616 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20273423 | C2 | semidirect |
| 4. #20273265 | C2 | semidirect |
| 5. #20273265 | C2 | semidirect |
| 6. #20273189 | C2 | semidirect |
| 9. Q8×Dic106 | C4 | semidirect |
| 10. #16811351 | C4 | semidirect |
| 13. #16811343 | C4 | semidirect |
| 15. #16811330 | C4 | semidirect |
| 289. C53 | #8501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289205 | 2 |
| #20273423 | 2 |
| #20273346 | 2 |
| #20273265 | 2 |
| #20273189 | 2 |
| C53×#1521 | 2 |
| #8501 | 53 |