Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
142 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 55 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. #20293032 | C2 | semidirect |
| 3. #20292455 | C2 | semidirect |
| 5. C4⋊C16×C107 | C2 | semidirect |
| 19. D856 | Q8 | semidirect |
| 56. C107 | #2226 | semidirect |
| 60. C4⋊C16 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293032 | 2 |
| C4×D856 | 2 |
| #20292455 | 2 |
| #20292429 | 2 |
| C4⋊C16×C107 | 2 |
| #2226 | 107 |