Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
224 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 69 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. #20293030 | C2 | semidirect |
| 3. #20293000 | C2 | semidirect |
| 4. #20292975 | C2 | semidirect |
| 5. #20292973 | C2 | semidirect |
| 6. C8×C107⋊C8 | C2 | semidirect |
| 7. #492×C107 | C2 | semidirect |
| 55. C8×C107 | D8 | semidirect |
| 57. C107⋊C8 | SD16 | semidirect |
| 76. C107 | #1706 | semidirect |
| 80. #492 | D107 | semidirect |
| 133. C8 | #13133803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293030 | 2 |
| #20293003 | 2 |
| #20293000 | 2 |
| #20292975 | 2 |
| #20292973 | 2 |
| C8×C107⋊C8 | 2 |
| #492×C107 | 2 |
| #1706 | 107 |