Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 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. #20292955 | C2 | semidirect |
| 4. #20292912 | C2 | semidirect |
| 5. #20292858 | C2 | semidirect |
| 6. #20292829 | C2 | semidirect |
| 7. #20292766 | C2 | semidirect |
| 8. C4×#13133805 | C2 | semidirect |
| 9. D4×C107⋊C8 | C2 | semidirect |
| 10. C2×#16812033 | C2 | semidirect |
| 11. D4×Q8×C107 | C2 | semidirect |
| 83. Q8×C107 | #41 | semidirect |
| 84. D4×C107 | SD16 | semidirect |
| 129. C107 | #3298 | semidirect |
| 130. D4×Q8 | D107 | semidirect |
| 213. Q8 | #13133817 | semidirect |
| 217. D4 | #13133805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293281 | 2 |
| #20292977 | 2 |
| #20292955 | 2 |
| #20292912 | 2 |
| #20292858 | 2 |
| #20292829 | 2 |
| #20292766 | 2 |
| C4×#13133805 | 2 |
| D4×C107⋊C8 | 2 |
| C2×#16812033 | 2 |
| D4×Q8×C107 | 2 |
| #3298 | 107 |