Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#19104781 | C2 | semidirect |
| 2. C2×#19104761 | C2 | semidirect |
| 3. C2×#19104731 | C2 | semidirect |
| 4. #23781831 | C2 | direct (N × H) |
| 5. C2×#19104662 | C2 | semidirect |
| 6. C2×#19104661 | C2 | semidirect |
| 7. C2×#19104651 | C2 | semidirect |
| 8. C2×AGL(1,ℤ/8)×C163 | C2 | semidirect |
| 12. #19104781 | C22 | semidirect |
| 22. #19104761 | C22 | semidirect |
| 25. C2×#14579683 | C22 | semidirect |
| 27. #19104731 | C22 | semidirect |
| 28. C2×C4×Dic163 | C22 | semidirect |
| 29. #19104662 | C22 | semidirect |
| 30. #19104661 | C22 | semidirect |
| 31. #19104651 | C22 | semidirect |
| 33. C22×D4×C163 | C22 | semidirect |
| 35. AGL(1,ℤ/8)×C163 | C22 | semidirect |
| 38. C2×M16×C163 | C22 | semidirect |
| 47. #14579699 | D4 | semidirect |
| 49. C2×Dic326 | D4 | semidirect |
| 58. C2×D652 | D4 | semidirect |
| 74. #14579683 | C23 | semidirect |
| 77. C4×Dic163 | C23 | semidirect |
| 81. #41×C163 | D4 | semidirect |
| 83. C2×Q8×C163 | D4 | semidirect |
| 90. C2×D4×C163 | D4 | semidirect |
| 91. C2×D4×C163 | C23 | semidirect |
| 97. M16×C163 | C23 | semidirect |
| 107. Dic326 | C2×D4 | semidirect |
| 114. D652 | C2×D4 | semidirect |
| 133. Q8×C163 | C2×D4 | semidirect |
| 141. D4×C163 | C2×D4 | semidirect |
| 180. C2×C163 | #453 | semidirect |
| 184. C163 | C2×#453 | semidirect |
| 188. C2×AGL(1,ℤ/8) | D163 | semidirect |
| 207. C22×D4 | C2×D163 | semidirect |
| 211. AGL(1,ℤ/8) | C2×D163 | semidirect |
| 217. C2×M16 | C2×D163 | semidirect |
| 237. #41 | C22⋊D163 | semidirect |
| 240. C2×Q8 | C22⋊D163 | semidirect |
| 265. C2×D4 | C22⋊D163 | semidirect |
| 266. C2×D4 | C22×D163 | semidirect |
| 279. M16 | C22×D163 | semidirect |
| 300. Q8 | C2×C22⋊D163 | semidirect |
| 319. D4 | C2×C22⋊D163 | semidirect |
| 367. C2 | #23781831 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104781 | 2 |
| C2×#19104761 | 2 |
| C2×#19104731 | 2 |
| #23781831 | 2 |
| C2×#19104662 | 2 |
| C2×#19104661 | 2 |
| C2×#19104651 | 2 |
| C2×AGL(1,ℤ/8)×C163 | 2 |
| C2×#453 | 163 |