Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16812727 | C2 | semidirect |
| 2. C2×#16812719 | C2 | semidirect |
| 3. #20295590 | C2 | semidirect |
| 4. #20295507 | C2 | semidirect |
| 5. #20295251 | C2 | semidirect |
| 6. #20295244 | C2 | semidirect |
| 7. #20295225 | C2 | semidirect |
| 8. #20295220 | C2 | semidirect |
| 9. #20295054 | C2 | semidirect |
| 10. C2×#16812619 | C2 | semidirect |
| 11. #417×C109 | C2 | semidirect |
| 16. C2×#13182019 | C22 | semidirect |
| 18. C2×#13182017 | C22 | semidirect |
| 19. C2×#13182016 | C22 | semidirect |
| 21. C2×#13182014 | C22 | semidirect |
| 28. #16812664 | C22 | semidirect |
| 29. #16812661 | C22 | semidirect |
| 34. #16812628 | C22 | semidirect |
| 35. #16812628 | C22 | semidirect |
| 41. #103×C109 | C22 | semidirect |
| 42. #102×C109 | C22 | semidirect |
| 45. #13182029 | D4 | semidirect |
| 155. C109 | #3045 | semidirect |
| 165. #417 | D109 | semidirect |
| 194. #103 | C2×D109 | semidirect |
| 197. #102 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812727 | 2 |
| C2×#16812719 | 2 |
| #20295590 | 2 |
| #20295507 | 2 |
| #20295251 | 2 |
| #20295244 | 2 |
| #20295225 | 2 |
| #20295220 | 2 |
| #20295054 | 2 |
| C2×#16812619 | 2 |
| #417×C109 | 2 |
| #3045 | 109 |