Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
426 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 139 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. #20293299 | C2 | semidirect |
| 2. Q8×D428 | C2 | semidirect |
| 3. #20292974 | C2 | semidirect |
| 4. #20292908 | C2 | semidirect |
| 5. #20292823 | C2 | semidirect |
| 6. C4×D856 | C2 | semidirect |
| 7. C8×Q8×C107 | C2 | semidirect |
| 46. Q8×C107 | D8 | semidirect |
| 57. D428 | #41 | semidirect |
| 82. C107 | #3358 | semidirect |
| 88. C8×Q8 | D107 | semidirect |
| 129. Q8 | D856 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293299 | 2 |
| Q8×D428 | 2 |
| #20292974 | 2 |
| #20292908 | 2 |
| #20292823 | 2 |
| C4×D856 | 2 |
| C8×Q8×C107 | 2 |
| #3358 | 107 |