Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
392 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 392 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. #20293184 | C2 | semidirect |
| 3. #20292996 | C2 | semidirect |
| 4. #20292992 | C2 | semidirect |
| 5. #20292987 | C2 | semidirect |
| 6. #20292624 | C2 | semidirect |
| 7. C2×#97×C107 | C2 | semidirect |
| 79. C107 | #3135 | semidirect |
| 86. C2×#97 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293184 | 2 |
| #20293177 | 2 |
| #20292996 | 2 |
| #20292992 | 2 |
| #20292987 | 2 |
| #20292624 | 2 |
| C2×#97×C107 | 2 |
| #3135 | 107 |