Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
1224 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 249 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. C24×Dic107 | C2 | semidirect |
| 3. C2×(C22⋊D107)⋊C4 | C2 | semidirect |
| 4. #20292504 | C2 | semidirect |
| 5. #20292499 | C2 | semidirect |
| 6. C22⋊C4×Dic107 | C2 | semidirect |
| 7. #379×C107 | C2 | semidirect |
| 12. C22×C4×D107 | C22 | semidirect |
| 13. #16812078 | C4 | semidirect |
| 15. C2×Dic107⋊C4 | C22 | semidirect |
| 17. C2×(C2×D107)⋊C4 | C22 | semidirect |
| 18. C2×C4×Dic107 | C22 | semidirect |
| 19. C107⋊#95 | C22 | semidirect |
| 26. C2×C22⋊D107 | C2×C4 | semidirect |
| 31. C22×Dic107 | D4 | semidirect |
| 37. C22⋊Dic107 | C2×C4 | semidirect |
| 42. C24×C107 | C2×C4 | semidirect |
| 59. C22×D107 | C22×C4 | semidirect |
| 69. C2×Dic107 | C22×C4 | semidirect |
| 78. C22×C107 | C4×D4 | semidirect |
| 89. Dic107 | #120 | semidirect |
| 96. C107 | C4×#120 | semidirect |
| 102. #379 | D107 | semidirect |
| 122. C24 | C4×D107 | semidirect |
| 177. C22 | (C22⋊D107)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic107 | 2 |
| C2×#16812078 | 2 |
| C2×(C22⋊D107)⋊C4 | 2 |
| #20292504 | 2 |
| #20292499 | 2 |
| C22⋊C4×Dic107 | 2 |
| #379×C107 | 2 |
| C4×#120 | 107 |