Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16812157 | C2 | semidirect |
| 2. C2×#16812135 | C2 | semidirect |
| 3. #20292799 | C2 | direct (N × H) |
| 4. C2×#16812037 | C2 | semidirect |
| 5. C2×#16812028 | C2 | semidirect |
| 6. C2×#124×C107 | C2 | semidirect |
| 9. #16812157 | C22 | semidirect |
| 15. #16812135 | C22 | semidirect |
| 19. #16812037 | C22 | semidirect |
| 20. #16812028 | C22 | semidirect |
| 24. #124×C107 | C22 | semidirect |
| 114. C2×C107 | #454 | semidirect |
| 118. C107 | C2×#454 | semidirect |
| 121. C2×#124 | D107 | semidirect |
| 140. #124 | C2×D107 | semidirect |
| 233. C2 | #20292799 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812157 | 2 |
| C2×#16812135 | 2 |
| #20292799 | 2 |
| C2×#16812037 | 2 |
| C2×#16812028 | 2 |
| C2×#124×C107 | 2 |
| C2×#454 | 107 |