Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 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. #20295657 | C2 | semidirect |
| 3. #20295389 | C2 | semidirect |
| 4. #20295384 | C2 | semidirect |
| 5. #20295379 | C2 | semidirect |
| 6. #20295371 | C2 | semidirect |
| 7. #20295031 | C2 | semidirect |
| 8. #20295025 | C2 | semidirect |
| 9. #20295023 | C2 | semidirect |
| 10. #20294981 | C2 | semidirect |
| 11. C2×#102×C109 | C2 | semidirect |
| 15. #16812698 | C22 | semidirect |
| 18. #16812690 | C22 | semidirect |
| 26. #16812624 | C22 | semidirect |
| 27. #16812624 | C22 | semidirect |
| 28. #16812622 | C22 | semidirect |
| 29. #16812621 | C22 | semidirect |
| 30. #16812621 | C22 | semidirect |
| 33. #16812619 | C22 | semidirect |
| 34. #16812609 | C22 | semidirect |
| 35. C8×Dic109 | C22 | semidirect |
| 136. C109 | #3136 | semidirect |
| 146. C2×#102 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295657 | 2 |
| #20295593 | 2 |
| #20295389 | 2 |
| #20295384 | 2 |
| #20295379 | 2 |
| #20295371 | 2 |
| #20295031 | 2 |
| #20295025 | 2 |
| #20295023 | 2 |
| #20294981 | 2 |
| C2×#102×C109 | 2 |
| #3136 | 109 |