Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
436 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#16812109 | C2 | semidirect |
| 2. #20292986 | C2 | direct (N × H) |
| 3. C2×#16812033 | C2 | semidirect |
| 5. C2×#16812020 | C2 | semidirect |
| 10. #16812109 | C22 | semidirect |
| 13. #16812033 | C22 | semidirect |
| 15. #16812020 | C22 | semidirect |
| 83. C2×C107 | #489 | semidirect |
| 88. C107 | C2×#489 | semidirect |
| 171. C2 | #20292986 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812109 | 2 |
| #20292986 | 2 |
| C2×#16812033 | 2 |
| C2×#16812030 | 2 |
| C2×#16812020 | 2 |
| C2×#124×C107 | 2 |
| C2×#489 | 107 |