Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 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. #20292924 | C2 | semidirect |
| 3. #20292914 | C2 | semidirect |
| 4. #20292904 | C2 | semidirect |
| 5. #20292670 | C2 | semidirect |
| 6. #20292651 | C2 | semidirect |
| 8. #533×C107 | C2 | semidirect |
| 18. #16812042 | C22 | semidirect |
| 19. #16812040 | C22 | semidirect |
| 20. C4⋊(C107⋊C8) | C22 | semidirect |
| 21. C4⋊(C107⋊C8) | C22 | semidirect |
| 24. C4⋊Q8×C107 | C22 | semidirect |
| 25. C4⋊Q8×C107 | C22 | semidirect |
| 26. #125×C107 | C22 | semidirect |
| 36. C2×D428 | Q8 | semidirect |
| 116. C107 | #3077 | semidirect |
| 117. #533 | D107 | semidirect |
| 128. C4⋊Q8 | C2×D107 | semidirect |
| 129. C4⋊Q8 | C2×D107 | semidirect |
| 130. #125 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D428 | 2 |
| #20292924 | 2 |
| #20292914 | 2 |
| #20292904 | 2 |
| #20292670 | 2 |
| #20292651 | 2 |
| #20292631 | 2 |
| #533×C107 | 2 |
| #3077 | 107 |