Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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. C22×#13133807 | C2 | semidirect |
| 3. #20293203 | C2 | semidirect |
| 4. #20293101 | C2 | semidirect |
| 5. #20292843 | C2 | semidirect |
| 6. #20292833 | C2 | semidirect |
| 7. #20292637 | C2 | semidirect |
| 8. #20292624 | C2 | semidirect |
| 9. #424×C107 | C2 | semidirect |
| 18. #16812109 | C22 | semidirect |
| 19. #16812097 | C22 | semidirect |
| 26. #16812034 | C22 | semidirect |
| 27. #16812034 | C22 | semidirect |
| 28. #16812031 | C22 | semidirect |
| 32. C4⋊C8×C107 | C22 | semidirect |
| 117. C107 | #3042 | semidirect |
| 124. #424 | D107 | semidirect |
| 146. C4⋊C8 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812137 | 2 |
| C22×#13133807 | 2 |
| #20293203 | 2 |
| #20293101 | 2 |
| #20292843 | 2 |
| #20292833 | 2 |
| #20292637 | 2 |
| #20292624 | 2 |
| #424×C107 | 2 |
| #3042 | 107 |