Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
166 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20293025 | C2 | semidirect |
| 4. #20292378 | C2 | semidirect |
| 5. #20292375 | C2 | semidirect |
| 6. #20292372 | C2 | semidirect |
| 57. C8×C107 | SD16 | semidirect |
| 77. C107 | #1671 | semidirect |
| 136. C8 | #13133806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293025 | 2 |
| #20292917 | 2 |
| #20292832 | 2 |
| #20292378 | 2 |
| #20292375 | 2 |
| #20292372 | 2 |
| C8×D4×C107 | 2 |
| #1671 | 107 |