Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
552 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 205 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×#16812074 | C2 | semidirect |
| 4. #20292714 | C2 | direct (N × H) |
| 5. C2×#16812032 | C2 | semidirect |
| 7. C2×C8×Dic107 | C2 | semidirect |
| 8. C2×#106×C107 | C2 | semidirect |
| 12. C2×#13133807 | C4 | semidirect |
| 16. #16812074 | C22 | semidirect |
| 23. #16812032 | C22 | semidirect |
| 25. C8×Dic107 | C22 | semidirect |
| 29. #106×C107 | C22 | semidirect |
| 33. C2×Dic214 | C2×C4 | semidirect |
| 44. #13133807 | C2×C4 | semidirect |
| 55. C2×C8×C107 | C2×C4 | semidirect |
| 77. C2×Dic107 | SD16 | semidirect |
| 86. Dic214 | C22×C4 | semidirect |
| 87. C8×C107 | C22×C4 | semidirect |
| 104. Dic107 | C2×SD16 | semidirect |
| 105. C2×C107 | C4×SD16 | semidirect |
| 111. C107 | C2×C4×SD16 | semidirect |
| 116. C2×#106 | D107 | semidirect |
| 137. #106 | C2×D107 | semidirect |
| 161. C2×C8 | C4×D107 | semidirect |
| 199. C8 | C2×C4×D107 | semidirect |
| 217. C2 | #20292714 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133807 | 2 |
| C2×#16812074 | 2 |
| C2×#16812071 | 2 |
| #20292714 | 2 |
| C2×#16812032 | 2 |
| C2×#16812029 | 2 |
| C2×C8×Dic107 | 2 |
| C2×#106×C107 | 2 |
| C2×C4×SD16 | 107 |