Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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. C22×#13133807 | C2 | semidirect |
| 3. C2×#16812096 | C2 | semidirect |
| 4. C2×#16812071 | C2 | semidirect |
| 5. #20292841 | C2 | direct (N × H) |
| 6. C2×Dic107⋊C8 | C2 | semidirect |
| 7. C2×#16812032 | C2 | semidirect |
| 8. C2×#102×C107 | C2 | semidirect |
| 13. C2×#13133807 | C22 | semidirect |
| 18. #16812096 | C22 | semidirect |
| 20. #16812071 | C22 | semidirect |
| 25. Dic107⋊C8 | C22 | semidirect |
| 26. #16812032 | C22 | semidirect |
| 30. #102×C107 | C22 | semidirect |
| 118. C2×C107 | #463 | semidirect |
| 124. C107 | C2×#463 | semidirect |
| 132. C2×#102 | D107 | semidirect |
| 154. #102 | C2×D107 | semidirect |
| 243. C2 | #20292841 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133807 | 2 |
| C22×#13133803 | 2 |
| C2×#16812096 | 2 |
| C2×#16812071 | 2 |
| #20292841 | 2 |
| C2×Dic107⋊C8 | 2 |
| C2×#16812032 | 2 |
| C2×#102×C107 | 2 |
| C2×#463 | 107 |