Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
1720 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 525 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. C22×#14268648 | C2 | semidirect |
| 2. C22×D4×D113 | C2 | semidirect |
| 3. C2×#16813649 | C2 | direct (N × H) |
| 4. C22×#14268634 | C2 | semidirect |
| 5. C22×D904 | C2 | semidirect |
| 6. C22×#14268632 | C2 | semidirect |
| 7. C22×#14268630 | C2 | semidirect |
| 8. C22×SD16×C113 | C2 | semidirect |
| 11. C2×#14268648 | C22 | semidirect |
| 14. C22×D452 | C22 | semidirect |
| 17. C2×D4×D113 | C22 | semidirect |
| 20. #16813649 | C22 | direct (N × H) |
| 21. C2×#14268634 | C22 | semidirect |
| 22. C2×D904 | C22 | semidirect |
| 23. C2×#14268632 | C22 | semidirect |
| 24. C2×#14268630 | C22 | semidirect |
| 25. C22×#11744751 | C22 | semidirect |
| 26. C22×Q8×C113 | C22 | semidirect |
| 28. C2×SD16×C113 | C22 | semidirect |
| 29. C22×C8×C113 | C22 | semidirect |
| 36. #14268648 | C23 | semidirect |
| 41. C2×D452 | C23 | semidirect |
| 44. D4×D113 | C23 | semidirect |
| 49. #14268634 | C23 | semidirect |
| 50. D904 | C23 | semidirect |
| 51. #14268632 | C23 | semidirect |
| 52. #14268630 | C23 | semidirect |
| 53. C2×#11744751 | C23 | semidirect |
| 56. C2×Q8×C113 | C23 | semidirect |
| 61. SD16×C113 | C23 | semidirect |
| 62. C2×C8×C113 | C23 | semidirect |
| 75. Q8×C113 | C24 | semidirect |
| 87. D452 | C24 | semidirect |
| 91. C8×C113 | C24 | semidirect |
| 92. #11744751 | C24 | semidirect |
| 95. C22×C113 | AGL(1,ℤ/8) | semidirect |
| 109. C2×C113 | C2×AGL(1,ℤ/8) | semidirect |
| 115. C113 | C22×AGL(1,ℤ/8) | semidirect |
| 120. C22×SD16 | D113 | semidirect |
| 127. C22×Q8 | C2×D113 | semidirect |
| 139. C2×SD16 | C2×D113 | semidirect |
| 144. C22×C8 | C2×D113 | semidirect |
| 154. C2×Q8 | C22×D113 | semidirect |
| 172. SD16 | C22×D113 | semidirect |
| 177. C2×C8 | C22×D113 | semidirect |
| 190. Q8 | C23×D113 | semidirect |
| 207. C8 | C23×D113 | semidirect |
| 217. C22 | #16813649 | direct (N × H) |
| 227. C2 | C2×#16813649 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14268648 | 2 |
| C22×D4×D113 | 2 |
| C2×#16813649 | 2 |
| C22×#14268634 | 2 |
| C22×D904 | 2 |
| C22×#14268632 | 2 |
| C22×#14268630 | 2 |
| C22×SD16×C113 | 2 |
| C22×AGL(1,ℤ/8) | 113 |