Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
716 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 716 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 |
|---|---|---|
| 2. C22×#13133162 | C2 | semidirect |
| 3. #20285210 | C2 | semidirect |
| 4. #20283566 | C2 | semidirect |
| 5. #20276769 | C2 | semidirect |
| 6. #20276759 | C2 | semidirect |
| 7. #20276473 | C2 | semidirect |
| 8. #20276434 | C2 | semidirect |
| 9. C53×#2138 | C2 | semidirect |
| 22. #16811006 | C22 | semidirect |
| 23. #16811001 | C22 | semidirect |
| 28. #16810441 | C22 | semidirect |
| 29. #16810426 | C22 | semidirect |
| 33. C53×#358 | C22 | semidirect |
| 34. C53×#357 | C22 | semidirect |
| 180. #2138 | D53 | semidirect |
| 209. #358 | C2×D53 | semidirect |
| 210. #357 | C2×D53 | semidirect |
| 211. C53 | #33586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811058 | 2 |
| C22×#13133162 | 2 |
| #20285210 | 2 |
| #20283566 | 2 |
| #20276769 | 2 |
| #20276759 | 2 |
| #20276473 | 2 |
| #20276434 | 2 |
| C53×#2138 | 2 |
| #33586 | 53 |