Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16812725 | C2 | semidirect |
| 2. C2×#16812719 | C2 | semidirect |
| 3. #20295506 | C2 | semidirect |
| 4. #20295245 | C2 | semidirect |
| 5. #20295238 | C2 | semidirect |
| 6. #20295223 | C2 | semidirect |
| 7. #20295218 | C2 | semidirect |
| 8. #20295053 | C2 | semidirect |
| 9. #20295027 | C2 | semidirect |
| 10. C2×#16812620 | C2 | semidirect |
| 11. #535×C109 | C2 | semidirect |
| 15. C2×#13182019 | C22 | semidirect |
| 17. C2×#13182017 | C22 | semidirect |
| 18. C2×#13182016 | C22 | semidirect |
| 20. C2×#13182014 | C22 | semidirect |
| 23. C4×Dic218 | C22 | semidirect |
| 24. C4×D436 | C22 | semidirect |
| 29. C4⋊#11724784 | C22 | semidirect |
| 30. C4⋊#11724784 | C22 | semidirect |
| 31. #16812623 | C22 | semidirect |
| 34. #16812620 | C22 | semidirect |
| 44. #13182029 | D4 | semidirect |
| 155. C109 | #3045 | semidirect |
| 158. #535 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812725 | 2 |
| C2×#16812719 | 2 |
| #20295506 | 2 |
| #20295245 | 2 |
| #20295238 | 2 |
| #20295223 | 2 |
| #20295218 | 2 |
| #20295053 | 2 |
| #20295027 | 2 |
| C2×#16812620 | 2 |
| #535×C109 | 2 |
| #3045 | 109 |