Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
460 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 3. #20292963 | C2 | direct (N × H) |
| 4. C2×#16812043 | C2 | semidirect |
| 5. C2×#16812034 | C2 | semidirect |
| 18. #16812043 | C22 | semidirect |
| 19. #16812034 | C22 | semidirect |
| 83. C2×C107 | #484 | semidirect |
| 88. C107 | C2×#484 | semidirect |
| 171. C2 | #20292963 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812088 | 2 |
| C22×C4⋊Dic107 | 2 |
| #20292963 | 2 |
| C2×#16812043 | 2 |
| C2×#16812034 | 2 |
| C2×C22⋊C8×C107 | 2 |
| C2×#484 | 107 |