Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
544 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×Q8×Dic107 | C2 | semidirect |
| 4. #20292730 | C2 | direct (N × H) |
| 5. C2×#16812042 | C2 | semidirect |
| 7. C2×#16812019 | C2 | semidirect |
| 8. C2×#103×C107 | C2 | semidirect |
| 11. C2×#13133805 | C4 | semidirect |
| 15. Q8×Dic107 | C22 | semidirect |
| 23. #16812042 | C22 | semidirect |
| 25. #16812019 | C22 | semidirect |
| 29. #103×C107 | C22 | semidirect |
| 40. #13133805 | C2×C4 | semidirect |
| 41. C2×C107⋊C8 | C2×C4 | semidirect |
| 52. C2×Q8×C107 | C2×C4 | semidirect |
| 68. Q8×C107 | C22×C4 | semidirect |
| 88. C107⋊C8 | C22×C4 | semidirect |
| 105. C2×C107 | #440 | semidirect |
| 111. C107 | C2×#440 | semidirect |
| 117. C2×#103 | D107 | semidirect |
| 138. #103 | C2×D107 | semidirect |
| 144. C2×Q8 | C4×D107 | semidirect |
| 179. Q8 | C2×C4×D107 | semidirect |
| 217. C2 | #20292730 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133805 | 2 |
| C2×Q8×Dic107 | 2 |
| C2×#16812071 | 2 |
| #20292730 | 2 |
| C2×#16812042 | 2 |
| C2×#16812031 | 2 |
| C2×#16812019 | 2 |
| C2×#103×C107 | 2 |
| C2×#440 | 107 |