Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
186 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 60 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. #19149612 | C4 | semidirect |
| 20. #19149612 | C4 | semidirect |
| 21. #19149611 | C4 | semidirect |
| 22. #106×C173 | C4 | semidirect |
| 88. C173 | #1922 | semidirect |
| 107. #106 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012498 | 2 |
| #26012456 | 2 |
| #26012367 | 2 |
| #26012361 | 2 |
| (C2×#10621924)⋊C8 | 2 |
| #26011526 | 2 |
| #1922 | 173 |