Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
2528 conjugacy classes of subgroups; only the 981 normal subgroups are shown.
This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 981 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 |
|---|---|---|
| 2. C23×C4×D173 | C2 | semidirect |
| 3. C2×C4×D692 | C2 | direct (N × H) |
| 4. C22×C4⋊Dic173 | C2 | semidirect |
| 5. C22×#14583803 | C2 | semidirect |
| 6. C22×C42×C173 | C2 | semidirect |
| 8. C22×D692 | C4 | direct (N × H) |
| 12. C22×C4×D173 | C22 | semidirect |
| 13. C4×D692 | C22 | direct (N × H) |
| 14. C2×C4⋊Dic173 | C22 | semidirect |
| 15. C2×#14583803 | C22 | semidirect |
| 19. C2×C42×C173 | C22 | semidirect |
| 22. C23×D173 | C2×C4 | semidirect |
| 24. C2×D692 | C2×C4 | direct (N × H) |
| 29. C2×C4×D173 | C23 | semidirect |
| 30. C4⋊Dic173 | C23 | semidirect |
| 31. #14583803 | C23 | semidirect |
| 34. C22×C4×C173 | C2×C4 | semidirect |
| 35. C22×C4×C173 | D4 | semidirect |
| 39. C42×C173 | C23 | semidirect |
| 43. C22×D173 | C22×C4 | semidirect |
| 45. D692 | C22×C4 | direct (N × H) |
| 54. C2×C4×C173 | C22×C4 | semidirect |
| 55. C2×C4×C173 | C2×D4 | semidirect |
| 59. C22×C173 | C4×D4 | semidirect |
| 67. C2×D173 | C23×C4 | semidirect |
| 69. C4×C173 | C23×C4 | semidirect |
| 70. C4×C173 | C22×D4 | semidirect |
| 72. C2×C173 | C2×C4×D4 | semidirect |
| 77. C173 | C22×C4×D4 | semidirect |
| 84. C22×C42 | D173 | semidirect |
| 97. C2×C42 | C2×D173 | semidirect |
| 110. C22×C4 | C4×D173 | semidirect |
| 111. C22×C4 | D692 | direct (N × H) |
| 117. C42 | C22×D173 | semidirect |
| 132. C2×C4 | C2×C4×D173 | semidirect |
| 133. C2×C4 | C2×D692 | direct (N × H) |
| 141. C22 | C4×D692 | direct (N × H) |
| 148. C4 | C22×C4×D173 | semidirect |
| 149. C4 | C22×D692 | direct (N × H) |
| 151. C2 | C2×C4×D692 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D692 | 2 |
| C23×C4×D173 | 2 |
| C2×C4×D692 | 2 |
| C22×C4⋊Dic173 | 2 |
| C22×#14583803 | 2 |
| C22×C42×C173 | 2 |
| C22×C4×D4 | 173 |