Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
292 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. #20295991 | C2 | semidirect |
| 4. C2×#16812753 | C2 | semidirect |
| 5. #20295902 | C2 | semidirect |
| 6. #20295896 | C2 | semidirect |
| 9. #16812787 | C4 | semidirect |
| 16. #16812764 | C4 | semidirect |
| 23. #16812623 | C4 | semidirect |
| 24. #16812621 | C4 | semidirect |
| 25. #16812619 | C4 | semidirect |
| 26. #103×C109 | C4 | semidirect |
| 110. C109 | #1765 | semidirect |
| 131. #103 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812787 | 2 |
| C2×#16812764 | 2 |
| #20295991 | 2 |
| C2×#16812753 | 2 |
| #20295902 | 2 |
| #20295896 | 2 |
| #20295021 | 2 |
| #1765 | 109 |