Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
544 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#16812107 | C2 | semidirect |
| 4. #20292830 | C2 | direct (N × H) |
| 5. C2×Dic107⋊C8 | C2 | semidirect |
| 6. C2×#16812034 | C2 | semidirect |
| 7. C2×#16812033 | C2 | semidirect |
| 15. #16812107 | C22 | semidirect |
| 23. Dic107⋊C8 | C22 | semidirect |
| 24. #16812034 | C22 | semidirect |
| 25. #16812033 | C22 | semidirect |
| 88. C2×Dic107 | SD16 | semidirect |
| 111. Dic107 | C2×SD16 | semidirect |
| 113. C2×C107 | #461 | semidirect |
| 118. C107 | C2×#461 | semidirect |
| 231. C2 | #20292830 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133806 | 2 |
| C2×#16812107 | 2 |
| C2×D4×Dic107 | 2 |
| #20292830 | 2 |
| C2×Dic107⋊C8 | 2 |
| C2×#16812034 | 2 |
| C2×#16812033 | 2 |
| C22×SD16×C107 | 2 |
| C2×#461 | 107 |