Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
314 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 59 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. #20293001 | C2 | semidirect |
| 3. #20292914 | C2 | semidirect |
| 4. #20292370 | C2 | semidirect |
| 5. D4⋊(C107⋊C8) | C2 | semidirect |
| 6. #20292354 | C2 | semidirect |
| 7. #476×C107 | C2 | semidirect |
| 17. C4⋊(C107⋊C8) | C22 | semidirect |
| 19. C4×C107⋊C8 | C22 | semidirect |
| 20. C4⋊Q8×C107 | C22 | semidirect |
| 23. C4⋊C8×C107 | C22 | semidirect |
| 60. D4×C107 | SD16 | semidirect |
| 77. D428 | SD16 | semidirect |
| 109. C107 | #1629 | semidirect |
| 113. #476 | D107 | semidirect |
| 120. C4⋊Q8 | C2×D107 | semidirect |
| 130. C4⋊C8 | C2×D107 | semidirect |
| 178. D4 | #13133805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D428 | 2 |
| #20293001 | 2 |
| #20292914 | 2 |
| #20292370 | 2 |
| D4⋊(C107⋊C8) | 2 |
| #20292354 | 2 |
| #476×C107 | 2 |
| #1629 | 107 |