Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 125 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×#16812132 | C2 | semidirect |
| 2. #20293280 | C2 | semidirect |
| 3. #20292865 | C2 | semidirect |
| 4. #20292829 | C2 | semidirect |
| 5. #20292788 | C2 | semidirect |
| 6. C4×D856 | C2 | semidirect |
| 7. C8×D428 | C2 | semidirect |
| 8. #494×C107 | C2 | semidirect |
| 38. D856 | D4 | semidirect |
| 85. C4×C107 | #135 | semidirect |
| 96. C107 | #3283 | semidirect |
| 99. #494 | D107 | semidirect |
| 183. C4 | #16812132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812132 | 2 |
| #20293280 | 2 |
| #20292865 | 2 |
| #20292829 | 2 |
| #20292788 | 2 |
| C4×D856 | 2 |
| C8×D428 | 2 |
| #494×C107 | 2 |
| #3283 | 107 |