Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 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. #20295862 | C2 | semidirect |
| 2. C2×#16812746 | C2 | semidirect |
| 3. #20295843 | C2 | semidirect |
| 4. #20295838 | C2 | semidirect |
| 5. #20295826 | C2 | semidirect |
| 6. C2×#16812732 | C2 | semidirect |
| 7. #568×C109 | C2 | semidirect |
| 10. #16812746 | C22 | semidirect |
| 11. #16812746 | C22 | semidirect |
| 12. #16812745 | C22 | semidirect |
| 15. C2×#13182029 | C22 | semidirect |
| 18. C22×Dic218 | C22 | semidirect |
| 20. #16812732 | C22 | semidirect |
| 21. #16812732 | C22 | semidirect |
| 22. #16812732 | C22 | semidirect |
| 23. #16812727 | C22 | semidirect |
| 24. #16812727 | C22 | semidirect |
| 25. #16812721 | C22 | semidirect |
| 26. C2×Dic436 | C22 | semidirect |
| 27. C2×#13182018 | C22 | semidirect |
| 29. #131×C109 | C22 | semidirect |
| 30. C2×M16×C109 | C22 | semidirect |
| 113. C109 | #3586 | semidirect |
| 120. #568 | D109 | semidirect |
| 142. #131 | C2×D109 | semidirect |
| 143. C2×M16 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295862 | 2 |
| C2×#16812746 | 2 |
| #20295843 | 2 |
| #20295838 | 2 |
| #20295826 | 2 |
| C2×#16812732 | 2 |
| #568×C109 | 2 |
| #3586 | 109 |