Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
348 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20292984 | C2 | semidirect |
| 4. #20292924 | C2 | semidirect |
| 5. #20292909 | C2 | semidirect |
| 6. #20292849 | C2 | semidirect |
| 8. Q8×C107⋊C8 | C2 | semidirect |
| 9. C4×#13133808 | C2 | semidirect |
| 10. C4×#13133805 | C2 | semidirect |
| 11. #557×C107 | C2 | semidirect |
| 118. C107 | #3365 | semidirect |
| 120. #557 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293362 | 2 |
| #20292984 | 2 |
| #20292975 | 2 |
| #20292924 | 2 |
| #20292909 | 2 |
| #20292849 | 2 |
| #20292827 | 2 |
| Q8×C107⋊C8 | 2 |
| C4×#13133808 | 2 |
| C4×#13133805 | 2 |
| #557×C107 | 2 |
| #3365 | 107 |