Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#16812706 | C2 | semidirect |
| 3. #20295590 | C2 | semidirect |
| 4. #20295277 | C2 | semidirect |
| 5. #20295274 | C2 | semidirect |
| 6. #20295260 | C2 | semidirect |
| 7. #20295257 | C2 | semidirect |
| 8. #20295066 | C2 | semidirect |
| 9. #20295022 | C2 | semidirect |
| 10. C2×#16812619 | C2 | semidirect |
| 11. #537×C109 | C2 | semidirect |
| 18. C2×#13182013 | C22 | semidirect |
| 20. C22×#11724784 | C22 | semidirect |
| 27. #16812632 | C22 | semidirect |
| 28. #16812630 | C22 | semidirect |
| 29. #16812623 | C22 | semidirect |
| 30. #16812623 | C22 | semidirect |
| 31. #16812620 | C22 | semidirect |
| 32. #16812620 | C22 | semidirect |
| 38. C22⋊Q8×C109 | C22 | semidirect |
| 41. #121×C109 | C22 | semidirect |
| 53. #13182013 | D4 | semidirect |
| 152. C109 | #3062 | semidirect |
| 155. #537 | D109 | semidirect |
| 178. C22⋊Q8 | C2×D109 | semidirect |
| 183. #121 | 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 |
| C2×#16812706 | 2 |
| #20295590 | 2 |
| #20295277 | 2 |
| #20295274 | 2 |
| #20295260 | 2 |
| #20295257 | 2 |
| #20295066 | 2 |
| #20295022 | 2 |
| C2×#16812619 | 2 |
| #537×C109 | 2 |
| #3062 | 109 |