Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
756 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 249 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. #20293394 | C2 | semidirect |
| 3. #20292609 | C2 | semidirect |
| 4. C2×#16812025 | C2 | semidirect |
| 5. #568×C107 | C2 | semidirect |
| 13. C2×#13133802 | C22 | semidirect |
| 14. #16812027 | C22 | semidirect |
| 15. #16812025 | C22 | semidirect |
| 18. C2×M16×C107 | C22 | semidirect |
| 77. C107 | #2888 | semidirect |
| 80. #568 | D107 | semidirect |
| 93. C2×M16 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812155 | 2 |
| #20293394 | 2 |
| #20292609 | 2 |
| C2×#16812025 | 2 |
| #568×C107 | 2 |
| #2888 | 107 |