Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #20292971 | C2 | semidirect |
| 4. #20292970 | C2 | semidirect |
| 5. #20292964 | C2 | semidirect |
| 6. #20292959 | C2 | semidirect |
| 7. #20292670 | C2 | semidirect |
| 8. #20292635 | C2 | semidirect |
| 9. C2×#16812034 | C2 | semidirect |
| 11. #427×C107 | C2 | semidirect |
| 127. C107 | #3097 | semidirect |
| 135. #427 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293203 | 2 |
| #20293107 | 2 |
| #20292971 | 2 |
| #20292970 | 2 |
| #20292964 | 2 |
| #20292959 | 2 |
| #20292670 | 2 |
| #20292635 | 2 |
| C2×#16812034 | 2 |
| #20292593 | 2 |
| #427×C107 | 2 |
| #3097 | 107 |