Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
414 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 2. C2×#16813580 | C2 | semidirect |
| 3. #20298942 | C2 | semidirect |
| 4. #20298941 | C2 | semidirect |
| 5. #20298925 | C2 | semidirect |
| 6. #20298924 | C2 | semidirect |
| 7. #20298641 | C2 | semidirect |
| 8. #20298600 | C2 | semidirect |
| 9. #20298597 | C2 | semidirect |
| 10. #20298561 | C2 | semidirect |
| 11. #428×C113 | C2 | semidirect |
| 30. #16813555 | C22 | semidirect |
| 31. #16813553 | C22 | semidirect |
| 32. #16813547 | C22 | semidirect |
| 33. #16813545 | C22 | semidirect |
| 34. #16813544 | C22 | semidirect |
| 35. #16813542 | C22 | semidirect |
| 41. #107×C113 | C22 | semidirect |
| 42. #106×C113 | C22 | semidirect |
| 153. C113 | #3093 | semidirect |
| 161. #428 | D113 | semidirect |
| 187. #107 | C2×D113 | semidirect |
| 189. #106 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299110 | 2 |
| C2×#16813580 | 2 |
| #20298942 | 2 |
| #20298941 | 2 |
| #20298925 | 2 |
| #20298924 | 2 |
| #20298641 | 2 |
| #20298600 | 2 |
| #20298597 | 2 |
| #20298561 | 2 |
| #428×C113 | 2 |
| #3093 | 113 |