Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20299251 | C2 | semidirect |
| 2. #20299233 | C2 | semidirect |
| 3. #20298910 | C2 | semidirect |
| 4. #20298875 | C2 | semidirect |
| 5. #20298833 | C2 | semidirect |
| 6. #20298790 | C2 | semidirect |
| 7. #20298733 | C2 | semidirect |
| 8. C4×D904 | C2 | semidirect |
| 9. C8×D452 | C2 | semidirect |
| 10. #102×D113 | C2 | semidirect |
| 11. #486×C113 | C2 | semidirect |
| 16. C2×#14268632 | C22 | semidirect |
| 17. C2×C8×D113 | C22 | semidirect |
| 20. #16813597 | C22 | semidirect |
| 26. C4×D452 | C22 | semidirect |
| 27. C4⋊C4×D113 | C22 | semidirect |
| 28. #16813556 | C22 | semidirect |
| 29. #16813555 | C22 | semidirect |
| 30. C4⋊#11744751 | C22 | semidirect |
| 32. #16813544 | C22 | semidirect |
| 33. #16813543 | C22 | semidirect |
| 35. #16813534 | C22 | semidirect |
| 36. C4⋊Q8×C113 | C22 | semidirect |
| 38. #102×C113 | C22 | semidirect |
| 39. #102×C113 | C22 | semidirect |
| 40. C4×C8×C113 | C22 | semidirect |
| 103. D452 | D8 | semidirect |
| 104. D452 | #41 | semidirect |
| 143. C113 | #3294 | semidirect |
| 146. #486 | D113 | semidirect |
| 161. C4⋊Q8 | C2×D113 | semidirect |
| 180. #102 | C2×D113 | semidirect |
| 181. #102 | C2×D113 | semidirect |
| 183. C4×C8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299251 | 2 |
| #20299233 | 2 |
| #20298910 | 2 |
| #20298875 | 2 |
| #20298833 | 2 |
| #20298790 | 2 |
| #20298733 | 2 |
| C4×D904 | 2 |
| C8×D452 | 2 |
| #102×D113 | 2 |
| #486×C113 | 2 |
| #3294 | 113 |