Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 205 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×C4×Dic214 | C2 | semidirect |
| 3. #20292532 | C2 | semidirect |
| 5. #20292515 | C2 | semidirect |
| 6. #20292500 | C2 | semidirect |
| 7. #20292496 | C2 | semidirect |
| 8. #20292473 | C2 | semidirect |
| 11. #16812096 | C4 | semidirect |
| 32. C2×Dic214 | C2×C4 | semidirect |
| 41. C22⋊Dic107 | C2×C4 | semidirect |
| 44. C4×Dic107 | C2×C4 | semidirect |
| 112. C107 | #2326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812096 | 2 |
| C2×C4×Dic214 | 2 |
| #20292532 | 2 |
| #20292530 | 2 |
| #20292515 | 2 |
| #20292500 | 2 |
| #20292496 | 2 |
| #20292473 | 2 |
| C2×C4×D4×C107 | 2 |
| #2326 | 107 |