Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
816 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 269 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×#13133802 | C2 | semidirect |
| 3. #20292626 | C2 | direct (N × H) |
| 4. C2×#16812032 | C2 | semidirect |
| 5. C2×#16812029 | C2 | semidirect |
| 6. C22×C4⋊C4×C107 | C2 | semidirect |
| 9. C2×#13133818 | C4 | semidirect |
| 16. C2×#13133802 | C22 | semidirect |
| 18. #16812032 | C22 | semidirect |
| 19. #16812029 | C22 | semidirect |
| 25. C2×C4⋊C4×C107 | C22 | semidirect |
| 29. #13133818 | C2×C4 | semidirect |
| 32. C2×Dic214 | C2×C4 | semidirect |
| 36. C2×D428 | C2×C4 | semidirect |
| 85. D428 | C22×C4 | semidirect |
| 89. Dic214 | C22×C4 | semidirect |
| 110. C2×C107 | #417 | semidirect |
| 116. C107 | C2×#417 | semidirect |
| 119. C22×C4⋊C4 | D107 | semidirect |
| 139. C2×C4⋊C4 | C2×D107 | semidirect |
| 227. C2 | #20292626 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133818 | 2 |
| C22×#13133802 | 2 |
| #20292626 | 2 |
| C2×#16812032 | 2 |
| C2×#16812029 | 2 |
| C22×C4⋊C4×C107 | 2 |
| C2×#417 | 107 |