Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#16812040 | C2 | semidirect |
| 4. #20292389 | C2 | semidirect |
| 11. C22⋊(C107⋊C8) | C4 | semidirect |
| 22. C2×C107⋊C8 | C2×C4 | semidirect |
| 74. C22×C107 | #106 | semidirect |
| 97. C107 | #1853 | semidirect |
| 171. C22 | #16812040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812040 | 2 |
| C2×C22⋊(C107⋊C8) | 2 |
| #20292487 | 2 |
| #20292389 | 2 |
| C22×C4⋊C4×C107 | 2 |
| #1853 | 107 |