Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
368 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 69 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×#16812024 | C2 | semidirect |
| 3. #20292419 | C2 | direct (N × H) |
| 4. C2×#99×C107 | C2 | semidirect |
| 5. C22×D428 | C4 | semidirect |
| 10. #16812105 | C4 | semidirect |
| 13. C2×C4×Dic107 | C4 | semidirect |
| 15. #16812024 | C22 | semidirect |
| 19. #99×C107 | C22 | semidirect |
| 24. C2×D428 | C2×C4 | semidirect |
| 36. C4×Dic107 | C2×C4 | semidirect |
| 117. C2×C107 | #353 | semidirect |
| 121. C107 | C2×#353 | semidirect |
| 124. C2×#99 | D107 | semidirect |
| 140. #99 | C2×D107 | semidirect |
| 239. C2 | #20292419 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812105 | 2 |
| C2×#16812024 | 2 |
| #20292419 | 2 |
| C2×#99×C107 | 2 |
| C2×#353 | 107 |