Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16812154 | C2 | semidirect |
| 2. C2×#16812135 | C2 | semidirect |
| 3. #20292794 | C2 | direct (N × H) |
| 4. C2×#16812037 | C2 | semidirect |
| 5. C2×#16812026 | C2 | semidirect |
| 6. C2×#127×C107 | C2 | semidirect |
| 9. #16812154 | C22 | semidirect |
| 15. #16812135 | C22 | semidirect |
| 18. C2×#13133802 | C22 | semidirect |
| 19. #16812037 | C22 | semidirect |
| 20. #16812026 | C22 | semidirect |
| 23. C22×D4×C107 | C22 | semidirect |
| 25. #127×C107 | C22 | semidirect |
| 26. C2×C42×C107 | C22 | semidirect |
| 30. #13133818 | D4 | semidirect |
| 34. C2×Dic214 | D4 | semidirect |
| 35. C2×D428 | D4 | semidirect |
| 47. #13133802 | C23 | semidirect |
| 60. C2×D4×C107 | C23 | semidirect |
| 64. C42×C107 | C23 | semidirect |
| 94. D428 | C2×D4 | semidirect |
| 98. Dic214 | C2×D4 | semidirect |
| 123. C2×C107 | #453 | semidirect |
| 127. C107 | C2×#453 | semidirect |
| 130. C2×#127 | D107 | semidirect |
| 143. C22×D4 | C2×D107 | semidirect |
| 150. #127 | C2×D107 | semidirect |
| 151. C2×C42 | C2×D107 | semidirect |
| 180. C2×D4 | C22×D107 | semidirect |
| 191. C42 | C22×D107 | semidirect |
| 251. C2 | #20292794 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812154 | 2 |
| C2×#16812135 | 2 |
| #20292794 | 2 |
| C2×#16812037 | 2 |
| C2×#16812026 | 2 |
| C2×#127×C107 | 2 |
| C2×#453 | 107 |