Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 61 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. C4×D856 | C2 | semidirect |
| 3. #20292454 | C2 | semidirect |
| 4. #20292428 | C2 | semidirect |
| 5. #20292427 | C2 | semidirect |
| 6. #20292403 | C2 | semidirect |
| 7. C4×D8×C107 | C2 | semidirect |
| 10. #16812050 | C4 | semidirect |
| 23. D856 | C2×C4 | semidirect |
| 27. C107⋊C16 | C2×C4 | semidirect |
| 31. D8×C107 | C2×C4 | semidirect |
| 72. C107 | #2177 | semidirect |
| 75. C4×D8 | D107 | semidirect |
| 99. D8 | C4×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812050 | 2 |
| C4×D856 | 2 |
| #20292454 | 2 |
| #20292428 | 2 |
| #20292427 | 2 |
| #20292403 | 2 |
| C4×D8×C107 | 2 |
| #2177 | 107 |