Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20293062 | C2 | semidirect |
| 2. C2×#16812052 | C2 | semidirect |
| 3. #20292897 | C2 | semidirect |
| 4. #20292443 | C2 | semidirect |
| 5. #20292434 | C2 | semidirect |
| 6. #20292411 | C2 | semidirect |
| 7. #578×C107 | C2 | semidirect |
| 91. C107 | #2193 | semidirect |
| 92. #578 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293062 | 2 |
| C2×#16812052 | 2 |
| #20292897 | 2 |
| #20292443 | 2 |
| #20292434 | 2 |
| #20292411 | 2 |
| #578×C107 | 2 |
| #2193 | 107 |