Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
392 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 392 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. #20292975 | C2 | semidirect |
| 3. #20292914 | C2 | semidirect |
| 4. #20292827 | C2 | semidirect |
| 5. Q8×C107⋊C8 | C2 | semidirect |
| 6. C4×#13133805 | C2 | semidirect |
| 7. Q82×C107 | C2 | semidirect |
| 46. Q8×C107 | SD16 | semidirect |
| 47. Q8×C107 | #41 | semidirect |
| 77. C107 | #3362 | semidirect |
| 78. Q82 | D107 | semidirect |
| 123. Q8 | #13133805 | semidirect |
| 124. Q8 | #13133819 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293299 | 2 |
| #20292975 | 2 |
| #20292914 | 2 |
| #20292827 | 2 |
| Q8×C107⋊C8 | 2 |
| C4×#13133805 | 2 |
| Q82×C107 | 2 |
| #3362 | 107 |