Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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×Dic107⋊C8 | C2 | semidirect |
| 4. #20292496 | C2 | semidirect |
| 5. #20292390 | C2 | semidirect |
| 6. #20292389 | C2 | semidirect |
| 11. D4×Dic107 | C4 | semidirect |
| 68. D4×C107 | C4⋊C4 | semidirect |
| 115. Dic107 | #102 | semidirect |
| 125. C107 | #1802 | semidirect |
| 193. D4 | Dic107⋊C4 | 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×Dic107⋊C8 | 2 |
| C2×#16812030 | 2 |
| #20292496 | 2 |
| #20292390 | 2 |
| #20292389 | 2 |
| C2×#102×C107 | 2 |
| #1802 | 107 |