Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
992 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 221 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×M16×D107 | C2 | semidirect |
| 3. C2×#16812026 | C2 | semidirect |
| 4. C2×#16812025 | C2 | semidirect |
| 5. #100×D107 | C2 | direct (N × H) |
| 6. C2×#100×C107 | C2 | semidirect |
| 16. C2×#13133802 | C22 | semidirect |
| 19. M16×D107 | C22 | semidirect |
| 21. #16812026 | C22 | semidirect |
| 22. #16812025 | C22 | semidirect |
| 24. C2×M16×C107 | C22 | semidirect |
| 25. #100×C107 | C22 | semidirect |
| 51. #13133802 | C23 | semidirect |
| 62. M16×C107 | C23 | semidirect |
| 119. C2×D107 | #100 | direct (N × H) |
| 128. C2×C107 | C2×#100 | semidirect |
| 132. D107 | C2×#100 | direct (N × H) |
| 134. C107 | C22×#100 | semidirect |
| 140. C2×#100 | D107 | direct (N × H) |
| 155. C2×M16 | C2×D107 | semidirect |
| 159. #100 | C2×D107 | direct (N × H) |
| 194. M16 | C22×D107 | semidirect |
| 265. C2 | #100×D107 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D107 | 2 |
| C2×M16×D107 | 2 |
| C2×#16812026 | 2 |
| C2×#16812025 | 2 |
| #100×D107 | 2 |
| C2×#100×C107 | 2 |
| C22×#100 | 107 |