Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 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×#16812724 | C2 | semidirect |
| 2. C22×D872 | C2 | semidirect |
| 3. #20295590 | C2 | semidirect |
| 4. #20295500 | C2 | semidirect |
| 5. #20295244 | C2 | semidirect |
| 6. #20295220 | C2 | semidirect |
| 7. #20295052 | C2 | semidirect |
| 8. #20295030 | C2 | semidirect |
| 9. #416×C109 | C2 | semidirect |
| 13. C2×#13182016 | C22 | semidirect |
| 16. C2×#13182014 | C22 | semidirect |
| 18. #16812695 | C22 | semidirect |
| 19. #16812688 | C22 | semidirect |
| 23. #16812661 | C22 | semidirect |
| 26. #16812628 | C22 | semidirect |
| 27. #16812619 | C22 | semidirect |
| 31. #103×C109 | C22 | semidirect |
| 32. #102×C109 | C22 | semidirect |
| 40. C2×D436 | D4 | semidirect |
| 122. C109 | #3041 | semidirect |
| 131. #416 | D109 | semidirect |
| 152. #103 | C2×D109 | semidirect |
| 154. #102 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812724 | 2 |
| C22×D872 | 2 |
| #20295590 | 2 |
| #20295500 | 2 |
| #20295244 | 2 |
| #20295220 | 2 |
| #20295052 | 2 |
| #20295030 | 2 |
| #416×C109 | 2 |
| #3041 | 109 |