Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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. #20293184 | C2 | semidirect |
| 3. #20293025 | C2 | semidirect |
| 4. #20293000 | C2 | semidirect |
| 5. #20292978 | C2 | semidirect |
| 6. #20292974 | C2 | semidirect |
| 7. #20292856 | C2 | semidirect |
| 8. C4×#13133807 | C2 | semidirect |
| 9. C2×C4×C8×C107 | C2 | semidirect |
| 71. C2×C4×C107 | SD16 | semidirect |
| 90. C8×C107 | #41 | semidirect |
| 113. C107 | #3167 | semidirect |
| 122. C2×C4×C8 | D107 | semidirect |
| 195. C2×C4 | #13133807 | semidirect |
| 203. C8 | #13133818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293184 | 2 |
| #20293177 | 2 |
| #20293025 | 2 |
| #20293000 | 2 |
| #20292978 | 2 |
| #20292974 | 2 |
| #20292856 | 2 |
| C4×#13133807 | 2 |
| C2×C4×C8×C107 | 2 |
| #3167 | 107 |