Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
1240 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 1240 conjugacy classes of subgroups — too many to draw. Only its 501 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. #20293363 | C2 | direct (N × H) |
| 2. C2×#16812096 | C2 | semidirect |
| 3. C2×#16812090 | C2 | semidirect |
| 4. C2×C4×Dic214 | C2 | semidirect |
| 5. C2×D4×Dic107 | C2 | semidirect |
| 9. #16812096 | C22 | semidirect |
| 10. #16812090 | C22 | semidirect |
| 11. C4×Dic214 | C22 | semidirect |
| 12. D4×Dic107 | C22 | semidirect |
| 68. C2×C107 | #559 | semidirect |
| 72. C107 | C2×#559 | semidirect |
| 140. C2 | #20293363 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293363 | 2 |
| C2×#16812096 | 2 |
| C2×#16812090 | 2 |
| C2×C4×Dic214 | 2 |
| C2×D4×Dic107 | 2 |
| C2×#127×C107 | 2 |
| C2×#559 | 107 |