Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 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. #20293239 | C2 | direct (N × H) |
| 2. C2×#16812109 | C2 | semidirect |
| 4. C2×#16812101 | C2 | semidirect |
| 5. C2×#16812099 | C2 | semidirect |
| 7. C2×C4×Dic214 | C2 | semidirect |
| 10. #16812109 | C22 | semidirect |
| 12. #16812101 | C22 | semidirect |
| 13. #16812099 | C22 | semidirect |
| 15. C4×Dic214 | C22 | semidirect |
| 82. C2×C107 | #541 | semidirect |
| 86. C107 | C2×#541 | semidirect |
| 168. C2 | #20293239 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293239 | 2 |
| C2×#16812109 | 2 |
| C2×#16812102 | 2 |
| C2×#16812101 | 2 |
| C2×#16812099 | 2 |
| C2×#16812088 | 2 |
| C2×C4×Dic214 | 2 |
| C2×#117×C107 | 2 |
| C2×#541 | 107 |