Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
334 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 77 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. #20292591 | C2 | semidirect |
| 3. #20292363 | C2 | semidirect |
| 4. #20292360 | C2 | semidirect |
| 5. C2×#95×C107 | C2 | semidirect |
| 6. C2×#13133818 | C4 | semidirect |
| 9. #16812088 | C4 | semidirect |
| 11. #16812083 | C4 | semidirect |
| 16. #16812068 | C4 | semidirect |
| 24. C2×Dic214 | C2×C4 | semidirect |
| 25. C2×D428 | C2×C4 | semidirect |
| 32. C4⋊Dic107 | C2×C4 | semidirect |
| 33. C4⋊Dic107 | C2×C4 | semidirect |
| 120. C107 | #1504 | semidirect |
| 123. C2×#95 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293138 | 2 |
| #20292591 | 2 |
| #20292363 | 2 |
| #20292360 | 2 |
| C2×#95×C107 | 2 |
| #1504 | 107 |