Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
402 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#16812033 | C2 | semidirect |
| 5. #20292389 | C2 | semidirect |
| 6. #20292382 | C2 | semidirect |
| 7. #391×C107 | C2 | semidirect |
| 12. C2×#13133805 | C4 | semidirect |
| 43. C2×C107⋊C8 | C2×C4 | semidirect |
| 52. C2×Q8×C107 | C2×C4 | semidirect |
| 85. C2×C4×C107 | SD16 | semidirect |
| 134. C107 | #1877 | semidirect |
| 139. #391 | D107 | semidirect |
| 166. C2×Q8 | C4×D107 | semidirect |
| 227. C2×C4 | #13133805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133805 | 2 |
| C2×C4×D428 | 2 |
| C2×#16812033 | 2 |
| C2×#16812029 | 2 |
| #20292389 | 2 |
| #20292382 | 2 |
| #391×C107 | 2 |
| #1877 | 107 |