Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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×#19149687 | C2 | semidirect |
| 2. C22×#14583809 | C2 | semidirect |
| 4. #26011568 | C2 | semidirect |
| 5. #26011561 | C2 | semidirect |
| 6. #26011457 | C2 | semidirect |
| 7. #26011454 | C2 | semidirect |
| 8. #26011447 | C2 | semidirect |
| 9. #424×C173 | C2 | semidirect |
| 17. C2×#14583809 | C22 | semidirect |
| 19. C2×C8×D173 | C22 | semidirect |
| 26. #19149591 | C22 | semidirect |
| 27. #19149590 | C22 | semidirect |
| 28. C4×#13063436 | C22 | semidirect |
| 32. C4⋊C8×C173 | C22 | semidirect |
| 50. C2×#13063436 | D4 | semidirect |
| 113. C173 | #2930 | semidirect |
| 120. #424 | D173 | semidirect |
| 142. C4⋊C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149687 | 2 |
| C22×#14583809 | 2 |
| #26012003 | 2 |
| #26011568 | 2 |
| #26011561 | 2 |
| #26011457 | 2 |
| #26011454 | 2 |
| #26011447 | 2 |
| #424×C173 | 2 |
| #2930 | 173 |