Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
480 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 157 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×#16812108 | C2 | semidirect |
| 3. #20292916 | C2 | direct (N × H) |
| 4. C2×#16812040 | C2 | semidirect |
| 5. C2×Dic107⋊C8 | C2 | semidirect |
| 8. C2×#106×C107 | C2 | semidirect |
| 14. #16812108 | C22 | semidirect |
| 21. #16812040 | C22 | semidirect |
| 22. Dic107⋊C8 | C22 | semidirect |
| 28. #106×C107 | C22 | semidirect |
| 34. C2×D428 | Q8 | semidirect |
| 79. D428 | C2×Q8 | semidirect |
| 100. C2×C107 | #476 | semidirect |
| 106. C107 | C2×#476 | semidirect |
| 111. C2×#106 | D107 | semidirect |
| 131. #106 | C2×D107 | semidirect |
| 207. C2 | #20292916 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812108 | 2 |
| C2×#16812071 | 2 |
| #20292916 | 2 |
| C2×#16812040 | 2 |
| C2×Dic107⋊C8 | 2 |
| C2×#16812031 | 2 |
| C2×#16812029 | 2 |
| C2×#106×C107 | 2 |
| C2×#476 | 107 |