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×#16812074 | C2 | semidirect |
| 4. #20292726 | C2 | direct (N × H) |
| 5. C2×#16812032 | C2 | semidirect |
| 7. C2×#16812019 | C2 | semidirect |
| 8. C2×#107×C107 | C2 | semidirect |
| 12. C2×#13133807 | C4 | semidirect |
| 16. #16812074 | C22 | semidirect |
| 23. #16812032 | C22 | semidirect |
| 25. #16812019 | C22 | semidirect |
| 29. #107×C107 | C22 | semidirect |
| 33. C2×Dic214 | C2×C4 | semidirect |
| 44. #13133807 | C2×C4 | semidirect |
| 55. C2×C8×C107 | C2×C4 | semidirect |
| 86. Dic214 | C22×C4 | semidirect |
| 87. C8×C107 | C22×C4 | semidirect |
| 105. C2×C107 | #440 | semidirect |
| 111. C107 | C2×#440 | semidirect |
| 116. C2×#107 | D107 | semidirect |
| 137. #107 | C2×D107 | semidirect |
| 161. C2×C8 | C4×D107 | semidirect |
| 199. C8 | C2×C4×D107 | semidirect |
| 217. C2 | #20292726 | 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 |
| #20292726 | 2 |
| C2×#16812032 | 2 |
| C2×#16812029 | 2 |
| C2×#16812019 | 2 |
| C2×#107×C107 | 2 |
| C2×#440 | 107 |