Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. #20295654 | C2 | semidirect |
| 2. #20295390 | C2 | semidirect |
| 3. #20295385 | C2 | semidirect |
| 4. #20295380 | C2 | semidirect |
| 5. #20295372 | C2 | semidirect |
| 6. #20295031 | C2 | semidirect |
| 7. #20295027 | C2 | semidirect |
| 8. #20295022 | C2 | semidirect |
| 9. C2×#16812620 | C2 | semidirect |
| 10. #20294982 | C2 | semidirect |
| 14. #16812699 | C22 | semidirect |
| 16. #16812691 | C22 | semidirect |
| 21. #16812623 | C22 | semidirect |
| 22. #16812623 | C22 | semidirect |
| 23. #16812623 | C22 | semidirect |
| 28. #16812620 | C22 | semidirect |
| 29. #16812620 | C22 | semidirect |
| 30. #16812620 | C22 | semidirect |
| 31. #16812610 | C22 | semidirect |
| 32. C4×#11724784 | C22 | semidirect |
| 136. C109 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295654 | 2 |
| #20295390 | 2 |
| #20295385 | 2 |
| #20295380 | 2 |
| #20295372 | 2 |
| #20295031 | 2 |
| #20295027 | 2 |
| #20295022 | 2 |
| C2×#16812620 | 2 |
| #20294982 | 2 |
| #535×C109 | 2 |
| #3136 | 109 |