Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20292955 | C2 | semidirect |
| 3. #20292914 | C2 | semidirect |
| 4. #20292829 | C2 | semidirect |
| 6. C4×#13133805 | C2 | semidirect |
| 7. #20292680 | C2 | semidirect |
| 8. #533×C107 | C2 | semidirect |
| 18. #16812040 | C22 | semidirect |
| 19. C4⋊(C107⋊C8) | C22 | semidirect |
| 20. #16812033 | C22 | semidirect |
| 23. C4×C107⋊C8 | C22 | semidirect |
| 24. C4⋊Q8×C107 | C22 | semidirect |
| 25. C4⋊Q8×C107 | C22 | semidirect |
| 30. C4×Q8×C107 | C22 | semidirect |
| 75. C2×C4×C107 | SD16 | semidirect |
| 113. C107 | #3101 | semidirect |
| 114. #533 | D107 | semidirect |
| 125. C4⋊Q8 | C2×D107 | semidirect |
| 126. C4⋊Q8 | C2×D107 | semidirect |
| 131. C4×Q8 | C2×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 |
|---|---|
| C2×C4×D428 | 2 |
| #20292955 | 2 |
| #20292914 | 2 |
| #20292829 | 2 |
| #20292777 | 2 |
| C4×#13133805 | 2 |
| #20292680 | 2 |
| #533×C107 | 2 |
| #3101 | 107 |