Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
424 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 2. C2×#16812109 | C2 | semidirect |
| 3. #20292987 | C2 | semidirect |
| 4. #20292978 | C2 | semidirect |
| 5. #20292974 | C2 | semidirect |
| 6. #20292629 | C2 | semidirect |
| 7. C4×M16×C107 | C2 | semidirect |
| 101. C107 | #3141 | semidirect |
| 108. C4×M16 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293177 | 2 |
| C2×#16812109 | 2 |
| #20292987 | 2 |
| #20292978 | 2 |
| #20292974 | 2 |
| #20292629 | 2 |
| C4×M16×C107 | 2 |
| #3141 | 107 |