Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 73 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. #20292751 | C2 | semidirect |
| 4. #20292377 | C2 | semidirect |
| 5. #20292359 | C2 | semidirect |
| 6. C8×C107⋊C8 | C2 | semidirect |
| 24. #13133806 | C8 | semidirect |
| 53. Dic214 | C2×C8 | semidirect |
| 59. C107⋊C8 | C2×C8 | semidirect |
| 60. C107⋊C8 | SD16 | semidirect |
| 78. C107 | C8×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20292751 | 2 |
| C4×#13133806 | 2 |
| D4×C107⋊C8 | 2 |
| #20292377 | 2 |
| #20292359 | 2 |
| C8×C107⋊C8 | 2 |
| D4⋊C8×C107 | 2 |
| C8×SD16 | 107 |