Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
1008 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 229 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. C22×#13133801 | C2 | semidirect |
| 3. C2×#16812067 | C2 | semidirect |
| 4. #20292630 | C2 | direct (N × H) |
| 5. C2×#16812031 | C2 | semidirect |
| 6. C2×#16812030 | C2 | semidirect |
| 7. C2×#16812029 | C2 | semidirect |
| 8. C2×#102×C107 | C2 | semidirect |
| 14. C2×D4×D107 | C4 | semidirect |
| 18. C2×#13133801 | C22 | semidirect |
| 19. C22×C107⋊C8 | C22 | semidirect |
| 21. #16812067 | C22 | semidirect |
| 22. C2×C4⋊Dic107 | C22 | semidirect |
| 25. #16812031 | C22 | semidirect |
| 26. #16812030 | C22 | semidirect |
| 27. #16812029 | C22 | semidirect |
| 29. C22×C8×C107 | C22 | semidirect |
| 30. C2×C4⋊C4×C107 | C22 | semidirect |
| 31. #102×C107 | C22 | semidirect |
| 46. D4×D107 | C2×C4 | semidirect |
| 55. C2×C107⋊C8 | C23 | semidirect |
| 57. C4⋊Dic107 | C23 | semidirect |
| 68. C2×C8×C107 | C23 | semidirect |
| 70. C4⋊C4×C107 | C23 | semidirect |
| 134. C2×C107 | #418 | semidirect |
| 141. C107 | C2×#418 | semidirect |
| 149. C2×#102 | D107 | semidirect |
| 162. C22×C8 | C2×D107 | semidirect |
| 166. C2×C4⋊C4 | C2×D107 | semidirect |
| 172. #102 | C2×D107 | semidirect |
| 205. C2×C8 | C22×D107 | semidirect |
| 209. C4⋊C4 | C22×D107 | semidirect |
| 277. C2 | #20292630 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D107 | 2 |
| C22×#13133801 | 2 |
| C2×#16812067 | 2 |
| #20292630 | 2 |
| C2×#16812031 | 2 |
| C2×#16812030 | 2 |
| C2×#16812029 | 2 |
| C2×#102×C107 | 2 |
| C2×#418 | 107 |