Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 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×#16812137 | C2 | semidirect |
| 2. C2×#16812106 | C2 | semidirect |
| 3. C4×#13133818 | C2 | semidirect |
| 4. #20292828 | C2 | semidirect |
| 5. #20292823 | C2 | semidirect |
| 6. #20292633 | C2 | semidirect |
| 7. #423×C107 | C2 | semidirect |
| 12. C2×#13133807 | C22 | semidirect |
| 13. C2×D856 | C22 | semidirect |
| 17. C4×Dic214 | C22 | semidirect |
| 18. C4×D428 | C22 | semidirect |
| 23. #16812031 | C22 | semidirect |
| 26. C4⋊C8×C107 | C22 | semidirect |
| 29. #13133818 | D4 | semidirect |
| 78. D428 | C2×D4 | semidirect |
| 82. Dic214 | C2×D4 | semidirect |
| 94. C4×C107 | AGL(1,ℤ/8) | semidirect |
| 105. C107 | #3038 | semidirect |
| 111. #423 | D107 | semidirect |
| 130. C4⋊C8 | C2×D107 | semidirect |
| 201. C4 | #16812137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812137 | 2 |
| C2×#16812106 | 2 |
| C4×#13133818 | 2 |
| #20292828 | 2 |
| #20292823 | 2 |
| #20292633 | 2 |
| #423×C107 | 2 |
| #3038 | 107 |