Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16812139 | C2 | semidirect |
| 2. C2×#16812115 | C2 | semidirect |
| 4. #20293203 | C2 | semidirect |
| 5. #20292884 | C2 | semidirect |
| 6. #20292872 | C2 | semidirect |
| 7. #20292867 | C2 | semidirect |
| 8. #20292855 | C2 | semidirect |
| 9. #20292670 | C2 | semidirect |
| 10. C2×#16812034 | C2 | semidirect |
| 11. #416×C107 | C2 | semidirect |
| 58. #13133802 | D4 | semidirect |
| 144. C107 | #3063 | semidirect |
| 154. #416 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812139 | 2 |
| C2×#16812115 | 2 |
| #20293205 | 2 |
| #20293203 | 2 |
| #20292884 | 2 |
| #20292872 | 2 |
| #20292867 | 2 |
| #20292855 | 2 |
| #20292670 | 2 |
| C2×#16812034 | 2 |
| #416×C107 | 2 |
| #3063 | 107 |