Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
146 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 56. C107⋊C8 | Q16 | semidirect |
| 71. C107 | #1692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293023 | 2 |
| #20292837 | 2 |
| #20292758 | 2 |
| #20292379 | 2 |
| #20292376 | 2 |
| #20292374 | 2 |
| #477×C107 | 2 |
| #1692 | 107 |