Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
216 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×D1712 | C2 | semidirect |
| 2. C2×#16812050 | C2 | semidirect |
| 3. #20293002 | C2 | semidirect |
| 4. C16×Dic107 | C2 | semidirect |
| 5. C2×D16×C107 | C2 | semidirect |
| 23. C107⋊C16 | D4 | semidirect |
| 28. C16×C107 | D4 | semidirect |
| 48. Dic107 | D16 | semidirect |
| 54. C107 | #2246 | semidirect |
| 57. C2×D16 | D107 | semidirect |
| 82. C16 | C22⋊D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D1712 | 2 |
| C2×#16812050 | 2 |
| #20293002 | 2 |
| C16×Dic107 | 2 |
| C2×D16×C107 | 2 |
| #2246 | 107 |