Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
726 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 253 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. #20295509 | C2 | semidirect |
| 3. #20295036 | C2 | semidirect |
| 4. #20295028 | C2 | semidirect |
| 5. #20295023 | C2 | semidirect |
| 6. C2×#16812624 | C2 | semidirect |
| 7. C2×#131×C109 | C2 | semidirect |
| 9. #16812746 | C4 | semidirect |
| 28. #13182029 | C2×C4 | semidirect |
| 32. C2×Dic218 | C2×C4 | semidirect |
| 95. C109 | #2898 | semidirect |
| 97. C2×#131 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812746 | 2 |
| #20295509 | 2 |
| #20295036 | 2 |
| #20295028 | 2 |
| #20295023 | 2 |
| C2×#16812624 | 2 |
| C2×#131×C109 | 2 |
| #2898 | 109 |