Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1252 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 253 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. C2×#19149641 | C2 | semidirect |
| 3. C2×C22⋊C4×D173 | C2 | semidirect |
| 4. #26011392 | C2 | semidirect |
| 5. #26011369 | C2 | semidirect |
| 6. #26011346 | C2 | semidirect |
| 7. C4×C22⋊Dic173 | C2 | semidirect |
| 8. #380×C173 | C2 | semidirect |
| 11. C22×D692 | C4 | semidirect |
| 15. C22×C4×D173 | C22 | semidirect |
| 19. C2×#14583803 | C22 | semidirect |
| 20. C2×#14583803 | C22 | semidirect |
| 21. C2×#14583803 | C22 | semidirect |
| 23. C2×C4×Dic173 | C22 | semidirect |
| 24. #19149586 | C22 | semidirect |
| 26. C2×C4⋊C4×C173 | C22 | semidirect |
| 28. #95×C173 | C22 | semidirect |
| 33. C23×D173 | C2×C4 | semidirect |
| 40. C2×D692 | C2×C4 | semidirect |
| 41. C2×D692 | C2×C4 | semidirect |
| 49. C22⋊Dic173 | D4 | semidirect |
| 56. C22×C4×C173 | C2×C4 | semidirect |
| 79. D692 | C22⋊C4 | semidirect |
| 85. C2×Dic173 | C2×D4 | semidirect |
| 105. C22×C173 | C4×D4 | semidirect |
| 121. C2×D173 | C2×C22⋊C4 | semidirect |
| 124. C4×C173 | C2×C22⋊C4 | semidirect |
| 135. C173 | D4×C22⋊C4 | semidirect |
| 142. #380 | D173 | semidirect |
| 154. C2×C4⋊C4 | C2×D173 | semidirect |
| 164. #95 | C2×D173 | semidirect |
| 186. C22×C4 | C4×D173 | semidirect |
| 252. C22 | #19149641 | semidirect |
| 262. C4 | C22⋊C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D692 | 2 |
| C2×#19149641 | 2 |
| C2×C22⋊C4×D173 | 2 |
| #26011392 | 2 |
| #26011369 | 2 |
| #26011346 | 2 |
| C4×C22⋊Dic173 | 2 |
| #380×C173 | 2 |
| D4×C22⋊C4 | 173 |