Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
500 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 185 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. #20293095 | C2 | semidirect |
| 3. #20292721 | C2 | semidirect |
| 4. #20292714 | C2 | semidirect |
| 5. #20292709 | C2 | semidirect |
| 6. #20292621 | C2 | semidirect |
| 7. C2×C8×Dic107 | C2 | semidirect |
| 8. #427×C107 | C2 | semidirect |
| 10. #16812131 | C4 | semidirect |
| 30. #13133818 | C2×C4 | semidirect |
| 37. Dic428 | C2×C4 | semidirect |
| 38. #13133807 | C2×C4 | semidirect |
| 39. D856 | C2×C4 | semidirect |
| 49. C2×C8×C107 | C2×C4 | semidirect |
| 87. Dic107 | #135 | semidirect |
| 93. C107 | C4×#135 | semidirect |
| 99. #427 | D107 | semidirect |
| 136. C2×C8 | C4×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812131 | 2 |
| #20293095 | 2 |
| #20292721 | 2 |
| #20292714 | 2 |
| #20292709 | 2 |
| #20292621 | 2 |
| C2×C8×Dic107 | 2 |
| #427×C107 | 2 |
| C4×#135 | 107 |