Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
210 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
| 4. #20292372 | C2 | semidirect |
| 5. Q8⋊(C107⋊C8) | C2 | semidirect |
| 6. #20292357 | C2 | semidirect |
| 51. Q8×C107 | SD16 | semidirect |
| 91. C107 | #1626 | semidirect |
| 146. Q8 | #13133806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293356 | 2 |
| #20292973 | 2 |
| #20292824 | 2 |
| #20292372 | 2 |
| Q8⋊(C107⋊C8) | 2 |
| #20292357 | 2 |
| #460×C107 | 2 |
| #1626 | 107 |