Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 125 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×#16812130 | C2 | semidirect |
| 2. #20293299 | C2 | semidirect |
| 3. #20293297 | C2 | semidirect |
| 4. #20293003 | C2 | semidirect |
| 5. #20292862 | C2 | semidirect |
| 6. #20292828 | C2 | semidirect |
| 7. #20292773 | C2 | semidirect |
| 8. #20292771 | C2 | semidirect |
| 9. C4×#13133808 | C2 | semidirect |
| 10. #20292692 | C2 | semidirect |
| 11. #460×C107 | C2 | semidirect |
| 58. #13133808 | D4 | semidirect |
| 130. C4×C107 | #135 | semidirect |
| 143. C107 | #3287 | semidirect |
| 150. #460 | D107 | semidirect |
| 276. C4 | #16812130 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812130 | 2 |
| #20293299 | 2 |
| #20293297 | 2 |
| #20293003 | 2 |
| #20292862 | 2 |
| #20292828 | 2 |
| #20292773 | 2 |
| #20292771 | 2 |
| C4×#13133808 | 2 |
| #20292692 | 2 |
| #460×C107 | 2 |
| #3287 | 107 |