Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 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. #20292931 | C2 | semidirect |
| 3. #20292924 | C2 | semidirect |
| 4. #20292919 | C2 | semidirect |
| 5. #20292904 | C2 | semidirect |
| 6. #20292670 | C2 | semidirect |
| 7. C2×#16812042 | C2 | semidirect |
| 8. #20292654 | C2 | semidirect |
| 11. #544×C107 | C2 | semidirect |
| 42. #13133818 | Q8 | semidirect |
| 124. C107 | #3083 | semidirect |
| 125. #544 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293107 | 2 |
| #20292931 | 2 |
| #20292924 | 2 |
| #20292919 | 2 |
| #20292904 | 2 |
| #20292670 | 2 |
| C2×#16812042 | 2 |
| #20292654 | 2 |
| #20292626 | 2 |
| #20292621 | 2 |
| #544×C107 | 2 |
| #3083 | 107 |