Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
544 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 205 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×C4×Dic214 | C2 | semidirect |
| 3. #20292727 | C2 | direct (N × H) |
| 4. C2×#16812042 | C2 | semidirect |
| 5. C2×#16812032 | C2 | semidirect |
| 7. C2×#16812020 | C2 | semidirect |
| 10. C2×#13133806 | C4 | semidirect |
| 15. C4×Dic214 | C22 | semidirect |
| 19. #16812042 | C22 | semidirect |
| 20. #16812032 | C22 | semidirect |
| 22. #16812020 | C22 | semidirect |
| 32. C2×Dic214 | C2×C4 | semidirect |
| 36. #13133806 | C2×C4 | semidirect |
| 38. C2×C107⋊C8 | C2×C4 | semidirect |
| 86. Dic214 | C22×C4 | semidirect |
| 88. C107⋊C8 | C22×C4 | semidirect |
| 106. C2×C107 | #440 | semidirect |
| 111. C107 | C2×#440 | semidirect |
| 217. C2 | #20292727 | 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×C4×Dic214 | 2 |
| #20292727 | 2 |
| C2×#16812042 | 2 |
| C2×#16812032 | 2 |
| C2×#16812030 | 2 |
| C2×#16812020 | 2 |
| C2×C4×D4×C107 | 2 |
| C2×#440 | 107 |