Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
448 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 157 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. #26011788 | C2 | direct (N × H) |
| 3. C2×#19149612 | C2 | semidirect |
| 4. C2×#19149610 | C2 | semidirect |
| 5. C2×C4⋊#13063436 | C2 | semidirect |
| 8. C2×#125×C173 | C2 | semidirect |
| 17. #19149612 | C22 | semidirect |
| 18. #19149610 | C22 | semidirect |
| 19. C4⋊#13063436 | C22 | semidirect |
| 23. #125×C173 | C22 | semidirect |
| 98. C2×C173 | #478 | semidirect |
| 103. C173 | C2×#478 | semidirect |
| 105. C2×#125 | D173 | semidirect |
| 118. #125 | C2×D173 | semidirect |
| 203. C2 | #26011788 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D692 | 2 |
| #26011788 | 2 |
| C2×#19149612 | 2 |
| C2×#19149610 | 2 |
| C2×C4⋊#13063436 | 2 |
| C2×#19149599 | 2 |
| C2×#125×C173 | 2 |
| C2×#478 | 173 |