Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
388 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 3. C2×#16812019 | C2 | semidirect |
| 4. C4⋊C4×Dic107 | C2 | semidirect |
| 5. #20292390 | C2 | semidirect |
| 6. #20292389 | C2 | semidirect |
| 11. D4×Dic107 | C4 | semidirect |
| 17. #16812030 | C4 | semidirect |
| 23. #102×C107 | C4 | semidirect |
| 33. C2×C107⋊C8 | C2×C4 | semidirect |
| 37. C4⋊Dic107 | C2×C4 | semidirect |
| 53. C2×C8×C107 | C2×C4 | semidirect |
| 55. C4⋊C4×C107 | C2×C4 | semidirect |
| 67. D4×C107 | C42 | semidirect |
| 124. C107 | #1762 | semidirect |
| 145. #102 | Dic107 | semidirect |
| 169. C2×C8 | C2×Dic107 | semidirect |
| 175. C4⋊C4 | C2×Dic107 | semidirect |
| 191. D4 | C4×Dic107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic107 | 2 |
| C2×#16812030 | 2 |
| C2×#16812019 | 2 |
| C4⋊C4×Dic107 | 2 |
| #20292390 | 2 |
| #20292389 | 2 |
| C2×#102×C107 | 2 |
| #1762 | 107 |