Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
488 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 488 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 |
|---|---|---|
| 2. C2×#16812101 | C2 | semidirect |
| 3. #20292992 | C2 | direct (N × H) |
| 4. C2×#16812031 | C2 | semidirect |
| 5. C2×#97×C107 | C2 | semidirect |
| 11. #16812101 | C22 | semidirect |
| 14. #16812031 | C22 | semidirect |
| 17. #97×C107 | C22 | semidirect |
| 59. C2×C107 | #490 | semidirect |
| 64. C107 | C2×#490 | semidirect |
| 69. C2×#97 | D107 | semidirect |
| 81. #97 | C2×D107 | semidirect |
| 124. C2 | #20292992 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812106 | 2 |
| C2×#16812101 | 2 |
| #20292992 | 2 |
| C2×#16812031 | 2 |
| C2×#97×C107 | 2 |
| C2×#490 | 107 |