Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
204 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20293004 | C2 | semidirect |
| 2. #20292822 | C2 | semidirect |
| 3. #20292380 | C2 | semidirect |
| 4. #20292370 | C2 | semidirect |
| 5. C8×D4×C107 | C2 | semidirect |
| 36. D4×C107 | D8 | semidirect |
| 50. C8×C107 | D8 | semidirect |
| 71. C107 | #1667 | semidirect |
| 74. C8×D4 | D107 | semidirect |
| 112. D4 | D856 | semidirect |
| 122. C8 | #13133803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293004 | 2 |
| #20292822 | 2 |
| #20292380 | 2 |
| #20292370 | 2 |
| C8×D4×C107 | 2 |
| #1667 | 107 |