Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
4544 conjugacy classes of subgroups; only the 661 normal subgroups are shown.
This group has 4544 conjugacy classes of subgroups — too many to draw. Only its 661 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. C25×D173 | C2 | semidirect |
| 2. C22×D4×D173 | C2 | semidirect |
| 3. C2×#19149649 | C2 | semidirect |
| 4. C2×#19149648 | C2 | semidirect |
| 5. C2×#19149647 | C2 | semidirect |
| 6. #120×D173 | C2 | direct (N × H) |
| 7. C2×C22⋊C4×D173 | C2 | semidirect |
| 8. C2×#120×C173 | C2 | semidirect |
| 11. C24×D173 | C22 | semidirect |
| 12. C24×D173 | C22 | semidirect |
| 13. C24×D173 | C22 | semidirect |
| 14. C22×D692 | C22 | semidirect |
| 15. C22×C22⋊D173 | C22 | semidirect |
| 16. C22×C22⋊D173 | C22 | semidirect |
| 18. C2×D4×D173 | C22 | semidirect |
| 19. C22×C4×D173 | C22 | semidirect |
| 20. #19149649 | C22 | semidirect |
| 21. #19149648 | C22 | semidirect |
| 22. #19149647 | C22 | semidirect |
| 23. C2×C22⋊Dic173 | C22 | semidirect |
| 24. C2×#14583803 | C22 | semidirect |
| 25. C22⋊C4×D173 | C22 | semidirect |
| 26. C25×C173 | C22 | semidirect |
| 27. C22×D4×C173 | C22 | semidirect |
| 28. #120×C173 | C22 | semidirect |
| 29. C2×C22⋊C4×C173 | C22 | semidirect |
| 36. C23×D173 | D4 | semidirect |
| 40. C23×D173 | C23 | semidirect |
| 41. C23×D173 | C23 | semidirect |
| 42. C23×D173 | C23 | semidirect |
| 44. C2×D692 | C23 | semidirect |
| 47. C2×C22⋊D173 | C23 | semidirect |
| 48. C2×C22⋊D173 | C23 | semidirect |
| 50. C22×Dic173 | C23 | semidirect |
| 52. C2×C4×D173 | C23 | semidirect |
| 53. C22⋊Dic173 | C23 | semidirect |
| 54. #14583803 | C23 | semidirect |
| 57. C24×C173 | C23 | semidirect |
| 58. C24×C173 | C23 | semidirect |
| 60. C2×D4×C173 | C23 | semidirect |
| 61. C22×C4×C173 | C23 | semidirect |
| 62. C22⋊C4×C173 | C23 | semidirect |
| 74. C22×D173 | C2×D4 | semidirect |
| 75. C22×D173 | C2×D4 | semidirect |
| 78. C22×D173 | C24 | semidirect |
| 83. C2×Dic173 | C24 | semidirect |
| 89. C23×C173 | C2×D4 | semidirect |
| 92. C23×C173 | C24 | semidirect |
| 95. C2×C4×C173 | C24 | semidirect |
| 102. C22×C173 | C22×D4 | semidirect |
| 111. C2×D173 | #120 | direct (N × H) |
| 113. C2×D173 | C22×D4 | semidirect |
| 118. C2×C173 | C2×#120 | semidirect |
| 122. D173 | C2×#120 | direct (N × H) |
| 123. C173 | C22×#120 | semidirect |
| 131. C2×#120 | D173 | direct (N × H) |
| 138. C25 | C2×D173 | semidirect |
| 144. C22×D4 | C2×D173 | semidirect |
| 149. #120 | C2×D173 | direct (N × H) |
| 153. C2×C22⋊C4 | C2×D173 | semidirect |
| 169. C24 | C22×D173 | semidirect |
| 170. C24 | C22×D173 | semidirect |
| 179. C2×D4 | C22×D173 | semidirect |
| 183. C22×C4 | C22×D173 | semidirect |
| 186. C22⋊C4 | C22×D173 | semidirect |
| 207. C23 | D4×D173 | semidirect |
| 210. C23 | C23×D173 | semidirect |
| 219. C2×C4 | C23×D173 | semidirect |
| 236. C22 | C2×D4×D173 | semidirect |
| 245. C2 | #120×D173 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×D173 | 2 |
| C22×D4×D173 | 2 |
| C2×#19149649 | 2 |
| C2×#19149648 | 2 |
| C2×#19149647 | 2 |
| #120×D173 | 2 |
| C2×C22⋊C4×D173 | 2 |
| C2×#120×C173 | 2 |
| C22×#120 | 173 |