Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
544 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 3. #20298696 | C2 | direct (N × H) |
| 4. C2×#16813555 | C2 | semidirect |
| 5. C2×#16813546 | C2 | semidirect |
| 7. C2×#16813533 | C2 | semidirect |
| 8. C2×C4×Q8×C113 | C2 | semidirect |
| 11. C2×#14268634 | C4 | semidirect |
| 19. #16813555 | C22 | semidirect |
| 20. #16813546 | C22 | semidirect |
| 22. #16813533 | C22 | semidirect |
| 25. C4×Q8×C113 | C22 | semidirect |
| 38. #14268634 | C2×C4 | semidirect |
| 40. C2×#11744751 | C2×C4 | semidirect |
| 48. C2×Q8×C113 | C2×C4 | semidirect |
| 68. Q8×C113 | C22×C4 | semidirect |
| 88. #11744751 | C22×C4 | semidirect |
| 105. C2×C113 | #440 | semidirect |
| 111. C113 | C2×#440 | semidirect |
| 113. C2×C4×Q8 | D113 | semidirect |
| 128. C4×Q8 | C2×D113 | semidirect |
| 144. C2×Q8 | C4×D113 | semidirect |
| 179. Q8 | C2×C4×D113 | semidirect |
| 217. C2 | #20298696 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14268634 | 2 |
| C2×C4×D452 | 2 |
| #20298696 | 2 |
| C2×#16813555 | 2 |
| C2×#16813546 | 2 |
| C2×#16813542 | 2 |
| C2×#16813533 | 2 |
| C2×C4×Q8×C113 | 2 |
| C2×#440 | 113 |