Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20299229 | C2 | semidirect |
| 3. #20298900 | C2 | semidirect |
| 4. #20298896 | C2 | semidirect |
| 5. #20298886 | C2 | semidirect |
| 6. #20298876 | C2 | semidirect |
| 7. #20298638 | C2 | semidirect |
| 8. #20298636 | C2 | semidirect |
| 9. #20298624 | C2 | semidirect |
| 14. #16813621 | C22 | semidirect |
| 16. #16813613 | C22 | semidirect |
| 26. #16813556 | C22 | semidirect |
| 27. #16813556 | C22 | semidirect |
| 28. #16813555 | C22 | semidirect |
| 29. #16813554 | C22 | semidirect |
| 30. #16813554 | C22 | semidirect |
| 31. #16813553 | C22 | semidirect |
| 32. #16813551 | C22 | semidirect |
| 33. #16813551 | C22 | semidirect |
| 66. C2×D4×C113 | Q8 | semidirect |
| 125. C113 | #3081 | semidirect |
| 170. C2×D4 | Dic226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299229 | 2 |
| #20299073 | 2 |
| #20298900 | 2 |
| #20298896 | 2 |
| #20298886 | 2 |
| #20298876 | 2 |
| #20298638 | 2 |
| #20298636 | 2 |
| #20298624 | 2 |
| #20298603 | 2 |
| C2×#102×C113 | 2 |
| #3081 | 113 |