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. Q8×D428 | C2 | semidirect |
| 2. #20292973 | C2 | semidirect |
| 3. #20292907 | C2 | semidirect |
| 4. #20292819 | C2 | semidirect |
| 5. Q8×C107⋊C8 | C2 | semidirect |
| 6. C4×#13133803 | C2 | semidirect |
| 7. #550×C107 | C2 | semidirect |
| 46. Q8×C107 | D8 | semidirect |
| 58. D428 | #41 | semidirect |
| 82. C107 | #3358 | semidirect |
| 83. #550 | D107 | semidirect |
| 129. Q8 | #13133803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D428 | 2 |
| #20292973 | 2 |
| #20292907 | 2 |
| #20292819 | 2 |
| Q8×C107⋊C8 | 2 |
| C4×#13133803 | 2 |
| #550×C107 | 2 |
| #3358 | 107 |