Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 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 |
|---|---|---|
| 1. C2×#16812134 | C2 | semidirect |
| 2. C2×C4×D428 | C2 | semidirect |
| 3. #20292839 | C2 | semidirect |
| 4. #20292829 | C2 | semidirect |
| 5. #20292819 | C2 | semidirect |
| 6. #20292651 | C2 | semidirect |
| 7. #20292628 | C2 | semidirect |
| 8. #532×C107 | C2 | semidirect |
| 21. C4⋊(C107⋊C8) | C22 | semidirect |
| 22. C4⋊(C107⋊C8) | C22 | semidirect |
| 23. #16812033 | C22 | semidirect |
| 24. #16812030 | C22 | semidirect |
| 26. C4⋊Q8×C107 | C22 | semidirect |
| 27. #127×C107 | C22 | semidirect |
| 28. #124×C107 | C22 | semidirect |
| 37. C2×D428 | D4 | semidirect |
| 119. C4×C107 | AGL(1,ℤ/8) | semidirect |
| 130. C107 | #3036 | semidirect |
| 132. #532 | D107 | semidirect |
| 146. C4⋊Q8 | C2×D107 | semidirect |
| 147. #127 | C2×D107 | semidirect |
| 148. #124 | C2×D107 | semidirect |
| 250. C4 | #16812134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812134 | 2 |
| C2×C4×D428 | 2 |
| #20292839 | 2 |
| #20292829 | 2 |
| #20292819 | 2 |
| #20292651 | 2 |
| #20292628 | 2 |
| #532×C107 | 2 |
| #3036 | 107 |