Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20292996 | C2 | semidirect |
| 4. #20292978 | C2 | semidirect |
| 68. C107 | #3139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293184 | 2 |
| C2×#16812109 | 2 |
| #20292996 | 2 |
| #20292978 | 2 |
| #20292637 | 2 |
| C4×M16×C107 | 2 |
| #3139 | 107 |