Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
180 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 3. #20292377 | C2 | semidirect |
| 4. Q8⋊(C107⋊C8) | C2 | semidirect |
| 6. C8×C107⋊C8 | C2 | semidirect |
| 7. C8×Q8×C107 | C2 | semidirect |
| 25. #13133805 | C8 | direct (N × H) |
| 43. Q8×C107 | C2×C8 | semidirect |
| 56. C8×C107 | SD16 | semidirect |
| 60. C107⋊C8 | C2×C8 | semidirect |
| 78. C107 | C8×SD16 | semidirect |
| 79. C8×Q8 | D107 | semidirect |
| 121. Q8 | C8×D107 | semidirect |
| 138. C8 | #13133805 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133805 | 2 |
| C8×D428 | 2 |
| #20292377 | 2 |
| Q8⋊(C107⋊C8) | 2 |
| #20292354 | 2 |
| C8×C107⋊C8 | 2 |
| C8×Q8×C107 | 2 |
| C8×SD16 | 107 |