Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#16812035 | C2 | semidirect |
| 3. #20292629 | C2 | semidirect |
| 4. #20292530 | C2 | semidirect |
| 5. C2×#100×C107 | C2 | semidirect |
| 8. #16812154 | C4 | semidirect |
| 13. C2×C4⋊Dic107 | C22 | semidirect |
| 15. C2×C4×Dic107 | C22 | semidirect |
| 20. C2×M16×C107 | C22 | semidirect |
| 80. D428 | C22⋊C4 | semidirect |
| 84. Dic214 | C22⋊C4 | semidirect |
| 113. C107 | #1792 | semidirect |
| 117. C2×#100 | D107 | semidirect |
| 127. C2×M16 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812154 | 2 |
| C2×#16812035 | 2 |
| #20292629 | 2 |
| #20292530 | 2 |
| C2×#100×C107 | 2 |
| #1792 | 107 |