Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 1. C22×C4⋊Dic107 | C2 | semidirect |
| 2. #20292938 | C2 | direct (N × H) |
| 3. C2×#16812042 | C2 | semidirect |
| 4. C2×#16812030 | C2 | semidirect |
| 5. C2×C22⋊(C107⋊C8) | C2 | semidirect |
| 12. C2×C4⋊Dic107 | C22 | semidirect |
| 13. #16812042 | C22 | semidirect |
| 14. #16812030 | C22 | semidirect |
| 15. C22⋊(C107⋊C8) | C22 | semidirect |
| 91. C2×C107 | #480 | semidirect |
| 96. C107 | C2×#480 | semidirect |
| 187. C2 | #20292938 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic107 | 2 |
| #20292938 | 2 |
| C2×#16812042 | 2 |
| C2×#16812030 | 2 |
| C2×C22⋊(C107⋊C8) | 2 |
| C2×#121×C107 | 2 |
| C2×#480 | 107 |