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. #20295387 | C2 | semidirect |
| 5. #20295382 | C2 | semidirect |
| 6. #20295371 | C2 | semidirect |
| 7. #20295032 | C2 | semidirect |
| 8. #20295022 | C2 | semidirect |
| 9. C2×#16812619 | C2 | semidirect |
| 10. #20294984 | C2 | semidirect |
| 11. #417×C109 | C2 | semidirect |
| 15. #16812698 | C22 | semidirect |
| 18. #16812690 | C22 | semidirect |
| 26. #16812623 | C22 | semidirect |
| 27. #16812623 | C22 | semidirect |
| 30. #16812620 | C22 | semidirect |
| 31. #16812620 | C22 | semidirect |
| 34. #16812609 | C22 | semidirect |
| 35. C8×Dic109 | C22 | semidirect |
| 39. #103×C109 | C22 | semidirect |
| 40. #102×C109 | C22 | semidirect |
| 136. C109 | #3136 | semidirect |
| 144. #417 | D109 | semidirect |
| 167. #103 | C2×D109 | semidirect |
| 174. #102 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295657 | 2 |
| #20295590 | 2 |
| #20295389 | 2 |
| #20295387 | 2 |
| #20295382 | 2 |
| #20295371 | 2 |
| #20295032 | 2 |
| #20295022 | 2 |
| C2×#16812619 | 2 |
| #20294984 | 2 |
| #417×C109 | 2 |
| #3136 | 109 |