Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. C22×#13133801 | C2 | semidirect |
| 3. C2×#16812031 | C2 | semidirect |
| 4. C2×#16812029 | C2 | semidirect |
| 5. #20292484 | C2 | semidirect |
| 6. #20292389 | C2 | semidirect |
| 7. #340×C107 | C2 | semidirect |
| 16. #16812084 | C4 | semidirect |
| 48. C2×C107⋊C8 | D4 | semidirect |
| 58. C2×C8×C107 | D4 | semidirect |
| 146. C107 | #1895 | semidirect |
| 153. #340 | D107 | semidirect |
| 200. C2×C8 | D428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133801 | 2 |
| C2×#16812084 | 2 |
| C2×#16812031 | 2 |
| C2×#16812029 | 2 |
| #20292484 | 2 |
| #20292389 | 2 |
| #340×C107 | 2 |
| #1895 | 107 |