Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20295840 | C2 | semidirect |
| 2. #20295837 | C2 | semidirect |
| 3. #20295409 | C2 | semidirect |
| 4. #20295301 | C2 | semidirect |
| 5. #20295293 | C2 | semidirect |
| 6. #20295287 | C2 | semidirect |
| 7. #20295204 | C2 | semidirect |
| 8. #20295197 | C2 | semidirect |
| 9. #20295143 | C2 | semidirect |
| 10. #20295141 | C2 | semidirect |
| 11. #576×C109 | C2 | semidirect |
| 12. #16812746 | C22 | semidirect |
| 15. #16812729 | C22 | semidirect |
| 18. #16812725 | C22 | semidirect |
| 22. C2×Dic436 | C22 | semidirect |
| 25. C2×#13182017 | C22 | semidirect |
| 26. #16812706 | C22 | semidirect |
| 27. #16812705 | C22 | semidirect |
| 28. #16812686 | C22 | semidirect |
| 29. #16812635 | C22 | semidirect |
| 30. #16812634 | C22 | semidirect |
| 32. #16812626 | C22 | semidirect |
| 33. #16812625 | C22 | semidirect |
| 34. #16812617 | C22 | semidirect |
| 35. #16812616 | C22 | semidirect |
| 36. C8×Dic109 | C22 | semidirect |
| 150. C109 | #3290 | semidirect |
| 153. #576 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295840 | 2 |
| #20295837 | 2 |
| #20295409 | 2 |
| #20295301 | 2 |
| #20295293 | 2 |
| #20295287 | 2 |
| #20295204 | 2 |
| #20295197 | 2 |
| #20295143 | 2 |
| #20295141 | 2 |
| #576×C109 | 2 |
| #3290 | 109 |