Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
1224 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 289 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 |
|---|---|---|
| 1. C24×Dic107 | C2 | semidirect |
| 2. C2×D4×Dic107 | C2 | semidirect |
| 3. #20292507 | C2 | semidirect |
| 4. #20292502 | C2 | semidirect |
| 5. #20292483 | C2 | semidirect |
| 6. C22⋊C4×Dic107 | C2 | semidirect |
| 11. C23×Dic107 | C22 | semidirect |
| 13. C2×C4⋊Dic107 | C22 | semidirect |
| 16. C2×C22⋊Dic107 | C22 | semidirect |
| 17. C2×C4×Dic107 | C22 | semidirect |
| 18. C107⋊#95 | C22 | semidirect |
| 21. #120×C107 | C4 | semidirect |
| 28. C22×Dic107 | D4 | semidirect |
| 40. C24×C107 | C2×C4 | semidirect |
| 45. C2×D4×C107 | C2×C4 | semidirect |
| 47. C22⋊C4×C107 | C2×C4 | semidirect |
| 56. C23×C107 | C22×C4 | semidirect |
| 63. C2×C4×C107 | C22×C4 | semidirect |
| 81. C22×C107 | C4×D4 | semidirect |
| 89. Dic107 | #120 | direct (N × H) |
| 96. C107 | C4×#120 | semidirect |
| 110. #120 | Dic107 | direct (N × H) |
| 121. C24 | C2×Dic107 | semidirect |
| 126. C2×D4 | C2×Dic107 | semidirect |
| 142. C22⋊C4 | C2×Dic107 | semidirect |
| 152. C23 | C22×Dic107 | semidirect |
| 168. C2×C4 | C22×Dic107 | semidirect |
| 177. C22 | D4×Dic107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic107 | 2 |
| C2×D4×Dic107 | 2 |
| #20292507 | 2 |
| #20292502 | 2 |
| #20292483 | 2 |
| C22⋊C4×Dic107 | 2 |
| C2×#120×C107 | 2 |
| C4×#120 | 107 |