Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
536 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 536 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 |
|---|---|---|
| 4. #20292668 | C2 | direct (N × H) |
| 5. C2×#16812042 | C2 | semidirect |
| 6. C2×#16812041 | C2 | semidirect |
| 7. C2×#16812040 | C2 | semidirect |
| 8. C2×#107×C107 | C2 | semidirect |
| 11. C2×#13133801 | C4 | semidirect |
| 23. #16812042 | C22 | semidirect |
| 24. #16812041 | C22 | semidirect |
| 25. #16812040 | C22 | semidirect |
| 29. #107×C107 | C22 | semidirect |
| 40. #13133801 | C2×C4 | semidirect |
| 41. C2×C107⋊C8 | C2×C4 | semidirect |
| 53. C2×C8×C107 | C2×C4 | semidirect |
| 82. C8×C107 | C22×C4 | semidirect |
| 83. C107⋊C8 | C22×C4 | semidirect |
| 100. C2×C107 | #428 | semidirect |
| 106. C107 | C2×#428 | semidirect |
| 112. C2×#107 | D107 | semidirect |
| 133. #107 | C2×D107 | semidirect |
| 152. C2×C8 | C4×D107 | semidirect |
| 189. C8 | C2×C4×D107 | semidirect |
| 207. C2 | #20292668 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133801 | 2 |
| C2×#16812067 | 2 |
| C2×C4⋊C4×D107 | 2 |
| #20292668 | 2 |
| C2×#16812042 | 2 |
| C2×#16812041 | 2 |
| C2×#16812040 | 2 |
| C2×#107×C107 | 2 |
| C2×#428 | 107 |