Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
996 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×#14583815 | C2 | semidirect |
| 3. C22×#14583814 | C2 | semidirect |
| 4. C2×#19149659 | C2 | semidirect |
| 5. #26011643 | C2 | direct (N × H) |
| 6. C2×#19149599 | C2 | semidirect |
| 7. C2×#19149591 | C2 | semidirect |
| 8. C2×#102×C173 | C2 | semidirect |
| 10. C22×Dic346 | C22 | semidirect |
| 19. C2×#14583815 | C22 | semidirect |
| 21. C2×#14583814 | C22 | semidirect |
| 22. C22×#13063436 | C22 | semidirect |
| 24. #19149659 | C22 | semidirect |
| 27. #19149599 | C22 | semidirect |
| 28. #19149591 | C22 | semidirect |
| 30. C22×C8×C173 | C22 | semidirect |
| 31. C2×C4⋊C4×C173 | C22 | semidirect |
| 32. #102×C173 | C22 | semidirect |
| 42. C2×Dic346 | C23 | semidirect |
| 61. C2×#13063436 | C23 | semidirect |
| 72. C2×C8×C173 | C23 | semidirect |
| 74. C4⋊C4×C173 | C23 | semidirect |
| 85. C22×D173 | SD16 | semidirect |
| 133. C2×D173 | C2×SD16 | semidirect |
| 141. C2×C173 | #450 | semidirect |
| 147. C173 | C2×#450 | semidirect |
| 155. C2×#102 | D173 | semidirect |
| 172. C22×C8 | C2×D173 | semidirect |
| 176. C2×C4⋊C4 | C2×D173 | semidirect |
| 179. #102 | C2×D173 | semidirect |
| 218. C2×C8 | C22×D173 | semidirect |
| 221. C4⋊C4 | C22×D173 | semidirect |
| 291. C2 | #26011643 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D173 | 2 |
| C22×#14583815 | 2 |
| C22×#14583814 | 2 |
| C2×#19149659 | 2 |
| #26011643 | 2 |
| C2×#19149599 | 2 |
| C2×#19149591 | 2 |
| C2×#102×C173 | 2 |
| C2×#450 | 173 |