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. #20298938 | C2 | semidirect |
| 4. #20298937 | C2 | semidirect |
| 5. #20298921 | C2 | semidirect |
| 6. #20298920 | C2 | semidirect |
| 7. #20298640 | C2 | semidirect |
| 8. #20298638 | C2 | semidirect |
| 9. #20298599 | C2 | semidirect |
| 10. #20298561 | C2 | semidirect |
| 11. #417×C113 | C2 | semidirect |
| 30. #16813556 | C22 | semidirect |
| 31. #16813555 | C22 | semidirect |
| 32. #16813554 | C22 | semidirect |
| 33. #16813553 | C22 | semidirect |
| 34. #16813546 | C22 | semidirect |
| 35. #16813543 | C22 | semidirect |
| 41. #103×C113 | C22 | semidirect |
| 42. #102×C113 | C22 | semidirect |
| 153. C113 | #3093 | semidirect |
| 163. #417 | D113 | semidirect |
| 191. #103 | C2×D113 | semidirect |
| 193. #102 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299105 | 2 |
| C2×#16813580 | 2 |
| #20298938 | 2 |
| #20298937 | 2 |
| #20298921 | 2 |
| #20298920 | 2 |
| #20298640 | 2 |
| #20298638 | 2 |
| #20298599 | 2 |
| #20298561 | 2 |
| #417×C113 | 2 |
| #3093 | 113 |