Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
136 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 7. C2×C107⋊C16 | C4 | semidirect |
| 9. #16812045 | C4 | semidirect |
| 56. C107 | #1383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812049 | 2 |
| C2×#16812045 | 2 |
| C2×#106×C107 | 2 |
| #1383 | 107 |