Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
218 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 4. #20292359 | C2 | semidirect |
| 5. Q8⋊(C107⋊C8) | C2 | semidirect |
| 6. #20292357 | C2 | semidirect |
| 7. Q8⋊C8×C107 | C2 | semidirect |
| 101. C107 | #1485 | semidirect |
| 108. Q8⋊C8 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293181 | 2 |
| #20292679 | 2 |
| C4×#13133801 | 2 |
| #20292359 | 2 |
| Q8⋊(C107⋊C8) | 2 |
| #20292357 | 2 |
| Q8⋊C8×C107 | 2 |
| #1485 | 107 |