Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#13133808 | C2 | semidirect |
| 3. #20293006 | C2 | semidirect |
| 4. #20292866 | C2 | semidirect |
| 5. #20292837 | C2 | semidirect |
| 6. #20292834 | C2 | semidirect |
| 7. #20292783 | C2 | semidirect |
| 8. #20292782 | C2 | semidirect |
| 9. C4×#13133808 | C2 | semidirect |
| 52. #13133808 | D4 | direct (N × H) |
| 88. D4×C107 | Q16 | semidirect |
| 113. C22×C107 | C2×Q16 | semidirect |
| 120. C4×C107 | C2×Q16 | semidirect |
| 131. C107 | D4×Q16 | semidirect |
| 224. D4 | #13133808 | direct (N × H) |
| 244. C22 | C2×#13133808 | semidirect |
| 254. C4 | C2×#13133808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133808 | 2 |
| D4×Dic214 | 2 |
| #20293006 | 2 |
| #20292866 | 2 |
| #20292837 | 2 |
| #20292834 | 2 |
| #20292783 | 2 |
| #20292782 | 2 |
| C4×#13133808 | 2 |
| D4×C107⋊C8 | 2 |
| D4×Q8×C107 | 2 |
| D4×Q16 | 107 |