Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
412 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16812100 | C2 | semidirect |
| 3. #20292983 | C2 | direct (N × H) |
| 4. C2×#16812033 | C2 | semidirect |
| 7. C2×C8×Dic107 | C2 | semidirect |
| 8. C2×#103×C107 | C2 | semidirect |
| 12. #16812100 | C22 | semidirect |
| 21. #16812033 | C22 | semidirect |
| 24. C8×Dic107 | C22 | semidirect |
| 28. #103×C107 | C22 | semidirect |
| 101. C2×C107 | #488 | semidirect |
| 107. C107 | C2×#488 | semidirect |
| 112. C2×#103 | D107 | semidirect |
| 132. #103 | C2×D107 | semidirect |
| 209. C2 | #20292983 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812100 | 2 |
| C2×#16812098 | 2 |
| #20292983 | 2 |
| C2×#16812033 | 2 |
| C2×#16812031 | 2 |
| C2×#16812029 | 2 |
| C2×C8×Dic107 | 2 |
| C2×#103×C107 | 2 |
| C2×#488 | 107 |