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×#16812727 | C2 | semidirect |
| 2. C2×#16812721 | C2 | semidirect |
| 3. #20295595 | C2 | semidirect |
| 4. #20295506 | C2 | semidirect |
| 5. #20295249 | C2 | semidirect |
| 6. #20295242 | C2 | semidirect |
| 7. #20295227 | C2 | semidirect |
| 8. #20295222 | C2 | semidirect |
| 9. #20295028 | C2 | semidirect |
| 10. C2×#16812621 | C2 | semidirect |
| 11. #424×C109 | C2 | semidirect |
| 17. C2×Dic436 | C22 | semidirect |
| 19. C2×#13182018 | C22 | semidirect |
| 20. C2×#13182018 | C22 | semidirect |
| 22. C2×D872 | C22 | semidirect |
| 28. C4×Dic218 | C22 | semidirect |
| 29. C4×D436 | C22 | semidirect |
| 34. #16812624 | C22 | semidirect |
| 37. #16812621 | C22 | semidirect |
| 41. C4⋊C8×C109 | C22 | semidirect |
| 42. C4⋊C8×C109 | C22 | semidirect |
| 47. #13182029 | D4 | semidirect |
| 155. C109 | #3045 | semidirect |
| 164. #424 | D109 | semidirect |
| 192. C4⋊C8 | C2×D109 | semidirect |
| 193. C4⋊C8 | 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×#16812721 | 2 |
| #20295595 | 2 |
| #20295506 | 2 |
| #20295249 | 2 |
| #20295242 | 2 |
| #20295227 | 2 |
| #20295222 | 2 |
| #20295028 | 2 |
| C2×#16812621 | 2 |
| #424×C109 | 2 |
| #3045 | 109 |