Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
230 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 19. #19149613 | C4 | semidirect |
| 20. #19149612 | C4 | semidirect |
| 21. #19149612 | C4 | semidirect |
| 22. #107×C173 | C4 | semidirect |
| 107. C173 | #1918 | semidirect |
| 128. #107 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012442 | 2 |
| C4⋊C4×#10621924 | 2 |
| #26012365 | 2 |
| #26012364 | 2 |
| (C2×#10621924)⋊C8 | 2 |
| #107×D173 | 2 |
| #1918 | 173 |