Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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. #20293180 | C2 | semidirect |
| 3. #20292994 | C2 | semidirect |
| 4. #20292990 | C2 | semidirect |
| 5. #20292988 | C2 | semidirect |
| 6. #20292985 | C2 | semidirect |
| 7. #20292624 | C2 | semidirect |
| 8. #20292623 | C2 | semidirect |
| 9. #20292621 | C2 | semidirect |
| 10. C2×#16812019 | C2 | semidirect |
| 11. #416×C107 | C2 | semidirect |
| 126. C107 | #3135 | semidirect |
| 136. #416 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293180 | 2 |
| #20293173 | 2 |
| #20292994 | 2 |
| #20292990 | 2 |
| #20292988 | 2 |
| #20292985 | 2 |
| #20292624 | 2 |
| #20292623 | 2 |
| #20292621 | 2 |
| C2×#16812019 | 2 |
| #416×C107 | 2 |
| #3135 | 107 |