Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
600 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 349 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. C2×#16812040 | C2 | direct (N × H) |
| 6. C22×C107⋊C8 | C4 | semidirect |
| 10. #16812040 | C22 | direct (N × H) |
| 17. C2×C107⋊C8 | C2×C4 | semidirect |
| 43. C107⋊C8 | C22×C4 | semidirect |
| 44. C22×C107 | #106 | semidirect |
| 54. C2×C107 | C2×#106 | semidirect |
| 59. C107 | C22×#106 | semidirect |
| 103. C22 | #16812040 | direct (N × H) |
| 113. C2 | C2×#16812040 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C107⋊C8 | 2 |
| C22×C4⋊Dic107 | 2 |
| C2×#16812040 | 2 |
| C22×C4⋊C4×C107 | 2 |
| C22×#106 | 107 |