Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
1224 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 277 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×C22⋊D107 | C2 | semidirect |
| 3. #20292506 | C2 | semidirect |
| 4. #20292500 | C2 | semidirect |
| 5. #20292483 | C2 | semidirect |
| 6. C4×C22⋊Dic107 | C2 | semidirect |
| 7. C24×C4×C107 | C2 | semidirect |
| 9. C22×C4×D107 | C22 | semidirect |
| 10. #16812078 | C4 | direct (N × H) |
| 12. C2×Dic107⋊C4 | C22 | semidirect |
| 16. C2×(C2×D107)⋊C4 | C22 | semidirect |
| 17. C2×C4×Dic107 | C22 | semidirect |
| 18. C107⋊#95 | C22 | semidirect |
| 26. C2×C22⋊D107 | C2×C4 | semidirect |
| 34. C22⋊Dic107 | C2×C4 | semidirect |
| 39. C24×C107 | C2×C4 | semidirect |
| 45. C22×C4×C107 | D4 | semidirect |
| 59. C22×D107 | C22×C4 | semidirect |
| 71. C2×Dic107 | C22×C4 | semidirect |
| 78. C22×C107 | C4×D4 | semidirect |
| 86. C4×C107 | #120 | semidirect |
| 96. C107 | C4×#120 | semidirect |
| 97. C24×C4 | D107 | semidirect |
| 122. C24 | C4×D107 | semidirect |
| 135. C22×C4 | C22⋊D107 | semidirect |
| 177. C22 | C4×C22⋊D107 | semidirect |
| 185. C4 | #16812078 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812078 | 2 |
| C2×C4×C22⋊D107 | 2 |
| #20292506 | 2 |
| #20292500 | 2 |
| #20292483 | 2 |
| C4×C22⋊Dic107 | 2 |
| C24×C4×C107 | 2 |
| C4×#120 | 107 |