Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
232 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 85 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×#16812049 | C2 | semidirect |
| 3. #20292436 | C2 | direct (N × H) |
| 4. C2×#106×C107 | C2 | semidirect |
| 8. #16812131 | C4 | semidirect |
| 10. C2×Dic428 | C4 | semidirect |
| 12. C2×D856 | C4 | semidirect |
| 14. #16812049 | C22 | semidirect |
| 19. #106×C107 | C22 | semidirect |
| 29. Dic428 | C2×C4 | semidirect |
| 33. D856 | C2×C4 | semidirect |
| 82. C2×C107 | #360 | semidirect |
| 86. C107 | C2×#360 | semidirect |
| 89. C2×#106 | D107 | semidirect |
| 105. #106 | C2×D107 | semidirect |
| 169. C2 | #20292436 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812131 | 2 |
| C2×#16812049 | 2 |
| #20292436 | 2 |
| C2×#106×C107 | 2 |
| C2×#360 | 107 |