Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 131 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×#16812132 | C2 | semidirect |
| 2. #20293296 | C2 | semidirect |
| 3. #20293002 | C2 | semidirect |
| 4. #20292863 | C2 | semidirect |
| 5. #20292860 | C2 | semidirect |
| 6. #20292825 | C2 | semidirect |
| 7. #20292772 | C2 | semidirect |
| 8. #20292771 | C2 | semidirect |
| 9. Q16×Dic107 | C2 | semidirect |
| 10. C8×C22⋊D107 | C2 | semidirect |
| 11. C2×#135×C107 | C2 | semidirect |
| 74. Q16×C107 | D4 | semidirect |
| 134. Dic107 | #135 | semidirect |
| 143. C107 | #3287 | semidirect |
| 145. C2×#135 | D107 | semidirect |
| 202. Q16 | C22⋊D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812132 | 2 |
| #20293296 | 2 |
| #20293002 | 2 |
| #20292863 | 2 |
| #20292860 | 2 |
| #20292825 | 2 |
| #20292772 | 2 |
| #20292771 | 2 |
| Q16×Dic107 | 2 |
| C8×C22⋊D107 | 2 |
| C2×#135×C107 | 2 |
| #3287 | 107 |