Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
740 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 205 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×C4×D428 | C2 | semidirect |
| 3. #20292529 | C2 | semidirect |
| 4. #20292505 | C2 | semidirect |
| 5. #20292493 | C2 | semidirect |
| 6. #376×C107 | C2 | semidirect |
| 10. #16812106 | C4 | semidirect |
| 24. C2×D428 | C2×C4 | semidirect |
| 25. C2×D428 | C2×C4 | semidirect |
| 37. C42×C107 | C2×C4 | semidirect |
| 38. C42×C107 | D4 | semidirect |
| 79. C107 | #2328 | semidirect |
| 85. #376 | D107 | semidirect |
| 116. C42 | C4×D107 | semidirect |
| 117. C42 | D428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812106 | 2 |
| C2×C4×D428 | 2 |
| #20292529 | 2 |
| #20292505 | 2 |
| #20292493 | 2 |
| #376×C107 | 2 |
| #2328 | 107 |