Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 2. C2×#16812054 | C2 | semidirect |
| 3. #20292868 | C2 | semidirect |
| 4. #20292429 | C2 | semidirect |
| 5. C22⋊C16×C107 | C2 | semidirect |
| 7. C2×Dic428 | C22 | semidirect |
| 13. #16812043 | C22 | semidirect |
| 16. C2×C16×C107 | C22 | semidirect |
| 55. C22×C107 | SD32 | semidirect |
| 72. C107 | #2187 | semidirect |
| 77. C22⋊C16 | D107 | semidirect |
| 86. C2×C16 | C2×D107 | semidirect |
| 131. C22 | #16812054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D856 | 2 |
| C2×#16812054 | 2 |
| #20292868 | 2 |
| #20292429 | 2 |
| C22⋊C16×C107 | 2 |
| #2187 | 107 |