Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
412 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20293023 | C2 | semidirect |
| 3. #20293001 | C2 | semidirect |
| 4. #20292977 | C2 | semidirect |
| 5. #20292975 | C2 | semidirect |
| 6. #20292858 | C2 | semidirect |
| 7. C4×#13133805 | C2 | semidirect |
| 8. C2×C4×C107⋊C8 | C2 | semidirect |
| 9. #533×C107 | C2 | semidirect |
| 75. C2×C4×C107 | SD16 | semidirect |
| 90. C107⋊C8 | #41 | semidirect |
| 113. C107 | #3167 | semidirect |
| 114. #533 | D107 | semidirect |
| 195. C2×C4 | #13133805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293177 | 2 |
| #20293023 | 2 |
| #20293001 | 2 |
| #20292977 | 2 |
| #20292975 | 2 |
| #20292858 | 2 |
| C4×#13133805 | 2 |
| C2×C4×C107⋊C8 | 2 |
| #533×C107 | 2 |
| #3167 | 107 |