Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20292977 | C2 | semidirect |
| 3. #20292960 | C2 | semidirect |
| 4. #20292922 | C2 | semidirect |
| 5. #20292866 | C2 | semidirect |
| 6. #20292834 | C2 | semidirect |
| 7. #20292783 | C2 | semidirect |
| 8. C4×#13133808 | C2 | semidirect |
| 10. C2×#16812033 | C2 | semidirect |
| 82. D4×C107 | Q16 | semidirect |
| 123. C107 | #3299 | semidirect |
| 208. D4 | #13133808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293334 | 2 |
| #20292977 | 2 |
| #20292960 | 2 |
| #20292922 | 2 |
| #20292866 | 2 |
| #20292834 | 2 |
| #20292783 | 2 |
| C4×#13133808 | 2 |
| D4×C107⋊C8 | 2 |
| C2×#16812033 | 2 |
| D4×Q8×C107 | 2 |
| #3299 | 107 |