Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
936 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 936 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. C22×C4×Dic107 | C2 | semidirect |
| 3. #20292532 | C2 | semidirect |
| 4. #20292528 | C2 | semidirect |
| 5. #20292504 | C2 | semidirect |
| 6. C4×(C2×D107)⋊C4 | C2 | semidirect |
| 7. C2×#117×C107 | C2 | semidirect |
| 10. C2×#13133818 | C4 | semidirect |
| 30. C2×Dic214 | C2×C4 | semidirect |
| 33. C2×D428 | C2×C4 | semidirect |
| 43. C2×C4×D107 | C2×C4 | semidirect |
| 68. C2×C4×C107 | C22⋊C4 | semidirect |
| 82. C2×Dic107 | #41 | semidirect |
| 110. C107 | #2297 | semidirect |
| 112. C2×#117 | D107 | semidirect |
| 189. C2×C4 | (C2×D107)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133818 | 2 |
| C22×C4×Dic107 | 2 |
| #20292532 | 2 |
| #20292528 | 2 |
| #20292504 | 2 |
| C4×(C2×D107)⋊C4 | 2 |
| C2×#117×C107 | 2 |
| #2297 | 107 |