Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
520 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 173 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. #20292531 | C2 | semidirect |
| 3. #20292519 | C2 | semidirect |
| 4. #20292517 | C2 | semidirect |
| 6. #20292501 | C2 | semidirect |
| 7. #20292498 | C2 | semidirect |
| 8. #20292493 | C2 | semidirect |
| 9. #382×C107 | C2 | semidirect |
| 13. #16812097 | C4 | semidirect |
| 35. C2×Dic214 | C2×C4 | semidirect |
| 51. (C2×D107)⋊C4 | C2×C4 | semidirect |
| 52. (C2×D107)⋊C4 | C2×C4 | semidirect |
| 61. C42×C107 | C2×C4 | semidirect |
| 128. C107 | #2379 | semidirect |
| 137. #382 | D107 | semidirect |
| 189. C42 | C4×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812097 | 2 |
| #20292531 | 2 |
| #20292519 | 2 |
| #20292517 | 2 |
| #20292505 | 2 |
| #20292501 | 2 |
| #20292498 | 2 |
| #20292493 | 2 |
| #382×C107 | 2 |
| #2379 | 107 |