Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
186 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 186 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. C2×#16812050 | C2 | semidirect |
| 2. C4×D856 | C2 | semidirect |
| 3. C4⋊(C107⋊C16) | C2 | semidirect |
| 4. #20292428 | C2 | semidirect |
| 5. #493×C107 | C2 | semidirect |
| 19. D856 | D4 | semidirect |
| 56. C4×C107 | D16 | semidirect |
| 66. C107 | #2206 | semidirect |
| 68. #493 | D107 | semidirect |
| 123. C4 | #16812050 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812050 | 2 |
| C4×D856 | 2 |
| C4⋊(C107⋊C16) | 2 |
| #20292428 | 2 |
| #493×C107 | 2 |
| #2206 | 107 |