Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
184 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 16. #16812044 | C4 | semidirect |
| 74. C107 | #1953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20292676 | 2 |
| #20292675 | 2 |
| C2×#16812044 | 2 |
| #20292583 | 2 |
| #20292397 | 2 |
| #344×C107 | 2 |
| #1953 | 107 |