Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
448 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 448 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. #20299318 | C2 | semidirect |
| 3. #20298945 | C2 | semidirect |
| 4. #20298923 | C2 | semidirect |
| 5. #20298879 | C2 | semidirect |
| 6. #20298844 | C2 | semidirect |
| 7. #20298799 | C2 | semidirect |
| 8. #20298751 | C2 | semidirect |
| 9. C4×#14268636 | C2 | semidirect |
| 10. #20298604 | C2 | semidirect |
| 11. #436×C113 | C2 | semidirect |
| 15. C2×#14268636 | C22 | semidirect |
| 16. #16813622 | C22 | semidirect |
| 20. #16813601 | C22 | semidirect |
| 24. C4×Dic226 | C22 | semidirect |
| 27. #16813581 | C22 | semidirect |
| 28. #16813556 | C22 | semidirect |
| 29. #16813554 | C22 | semidirect |
| 30. #16813547 | C22 | semidirect |
| 33. #16813544 | C22 | semidirect |
| 34. #16813544 | C22 | semidirect |
| 35. #16813544 | C22 | semidirect |
| 36. C2×M16×C113 | C22 | semidirect |
| 38. C4⋊C8×C113 | C22 | semidirect |
| 39. C22⋊C8×C113 | C22 | semidirect |
| 40. C4×C8×C113 | C22 | semidirect |
| 136. C113 | #3324 | semidirect |
| 146. #436 | D113 | semidirect |
| 152. C2×M16 | C2×D113 | semidirect |
| 168. C4⋊C8 | C2×D113 | semidirect |
| 175. C22⋊C8 | C2×D113 | semidirect |
| 176. C4×C8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299318 | 2 |
| D4×D452 | 2 |
| #20298945 | 2 |
| #20298923 | 2 |
| #20298879 | 2 |
| #20298844 | 2 |
| #20298799 | 2 |
| #20298751 | 2 |
| C4×#14268636 | 2 |
| #20298604 | 2 |
| #436×C113 | 2 |
| #3324 | 113 |