Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 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 |
|---|---|---|
| 1. C2×#16812156 | C2 | semidirect |
| 2. C2×#16812134 | C2 | semidirect |
| 3. C22×#13133807 | C2 | semidirect |
| 4. #20293196 | C2 | semidirect |
| 5. #20292773 | C2 | semidirect |
| 6. #20292767 | C2 | semidirect |
| 7. #20292635 | C2 | semidirect |
| 8. #20292593 | C2 | semidirect |
| 9. #416×C107 | C2 | semidirect |
| 15. C2×#13133817 | C22 | semidirect |
| 18. C2×Q8×D107 | C22 | semidirect |
| 30. #16812032 | C22 | semidirect |
| 31. (C2×D107)⋊C8 | C22 | semidirect |
| 35. #103×C107 | C22 | semidirect |
| 36. #102×C107 | C22 | semidirect |
| 49. C2×Dic214 | D4 | semidirect |
| 72. #41×C107 | D4 | semidirect |
| 146. C107 | #3010 | semidirect |
| 154. #416 | D107 | semidirect |
| 180. #103 | C2×D107 | semidirect |
| 181. #102 | C2×D107 | semidirect |
| 191. #41 | D428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812156 | 2 |
| C2×#16812134 | 2 |
| C22×#13133807 | 2 |
| #20293196 | 2 |
| #20292773 | 2 |
| #20292767 | 2 |
| #20292635 | 2 |
| #20292593 | 2 |
| #416×C107 | 2 |
| #3010 | 107 |