Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
382 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20293356 | C2 | semidirect |
| 3. #20292990 | C2 | semidirect |
| 4. #20292974 | C2 | semidirect |
| 5. #20292926 | C2 | semidirect |
| 6. #20292907 | C2 | semidirect |
| 7. #20292827 | C2 | semidirect |
| 8. #20292825 | C2 | semidirect |
| 9. #20292757 | C2 | semidirect |
| 10. #20292730 | C2 | semidirect |
| 11. C4×SD16×C107 | C2 | semidirect |
| 77. Q8×C107 | #41 | semidirect |
| 125. C107 | #3368 | semidirect |
| 136. C4×SD16 | D107 | semidirect |
| 204. Q8 | #13133818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293356 | 2 |
| #20293298 | 2 |
| #20292990 | 2 |
| #20292974 | 2 |
| #20292926 | 2 |
| #20292907 | 2 |
| #20292827 | 2 |
| #20292825 | 2 |
| #20292757 | 2 |
| #20292730 | 2 |
| C4×SD16×C107 | 2 |
| #3368 | 107 |