Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#13133817 | C2 | semidirect |
| 2. C22×#13133807 | C2 | semidirect |
| 3. C22×#13133803 | C2 | semidirect |
| 4. C2×#16812084 | C2 | semidirect |
| 5. #20292773 | C2 | direct (N × H) |
| 6. C2×#16812032 | C2 | semidirect |
| 7. C2×(C2×D107)⋊C8 | C2 | semidirect |
| 8. C2×#102×C107 | C2 | semidirect |
| 12. C2×#13133817 | C22 | semidirect |
| 20. C2×#13133807 | C22 | semidirect |
| 22. C2×#13133803 | C22 | semidirect |
| 25. #16812084 | C22 | semidirect |
| 27. #16812032 | C22 | semidirect |
| 28. (C2×D107)⋊C8 | C22 | semidirect |
| 32. #102×C107 | C22 | semidirect |
| 40. C2×Dic214 | D4 | semidirect |
| 66. C2×D4×C107 | D4 | semidirect |
| 89. D4×C107 | C2×D4 | semidirect |
| 111. Dic214 | C2×D4 | semidirect |
| 137. C2×C107 | #449 | semidirect |
| 144. C107 | C2×#449 | semidirect |
| 151. C2×#102 | D107 | semidirect |
| 175. #102 | C2×D107 | semidirect |
| 197. C2×D4 | D428 | semidirect |
| 241. D4 | C2×D428 | semidirect |
| 283. C2 | #20292773 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133817 | 2 |
| C22×#13133807 | 2 |
| C22×#13133803 | 2 |
| C2×#16812084 | 2 |
| #20292773 | 2 |
| C2×#16812032 | 2 |
| C2×(C2×D107)⋊C8 | 2 |
| C2×#102×C107 | 2 |
| C2×#449 | 107 |