Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
526 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 526 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. C2×#16813645 | C2 | semidirect |
| 2. C2×D8×D113 | C2 | semidirect |
| 3. #20299241 | C2 | semidirect |
| 4. #20298836 | C2 | semidirect |
| 5. #20298831 | C2 | semidirect |
| 6. #20298810 | C2 | semidirect |
| 7. #20298747 | C2 | semidirect |
| 8. #20298742 | C2 | semidirect |
| 9. C4×D904 | C2 | semidirect |
| 10. C8×D452 | C2 | semidirect |
| 11. #495×C113 | C2 | semidirect |
| 12. C2×#14268648 | C22 | semidirect |
| 15. C2×#14268634 | C22 | semidirect |
| 20. C2×C8×D113 | C22 | semidirect |
| 24. #16813593 | C22 | semidirect |
| 27. C4×D452 | C22 | semidirect |
| 29. #16813556 | C22 | semidirect |
| 30. C4⋊#11744751 | C22 | semidirect |
| 31. #16813546 | C22 | semidirect |
| 32. #16813544 | C22 | semidirect |
| 33. #16813543 | C22 | semidirect |
| 35. #16813534 | C22 | semidirect |
| 36. C2×Q16×C113 | C22 | semidirect |
| 37. C2×SD16×C113 | C22 | semidirect |
| 39. #124×C113 | C22 | semidirect |
| 40. C4×C8×C113 | C22 | semidirect |
| 56. D904 | D4 | semidirect |
| 127. C2×D113 | #135 | semidirect |
| 144. C113 | #3280 | semidirect |
| 148. #495 | D113 | semidirect |
| 159. C2×Q16 | C2×D113 | semidirect |
| 161. C2×SD16 | C2×D113 | semidirect |
| 168. #124 | C2×D113 | semidirect |
| 184. C4×C8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813645 | 2 |
| C2×D8×D113 | 2 |
| #20299241 | 2 |
| #20298836 | 2 |
| #20298831 | 2 |
| #20298810 | 2 |
| #20298747 | 2 |
| #20298742 | 2 |
| C4×D904 | 2 |
| C8×D452 | 2 |
| #495×C113 | 2 |
| #3280 | 113 |