Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
336 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 78 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×#19149742 | C2 | semidirect |
| 3. C4×D173⋊C8 | C2 | semidirect |
| 4. #26012435 | C2 | semidirect |
| 14. #19149668 | C4 | semidirect |
| 15. #19149667 | C4 | semidirect |
| 16. #19149666 | C4 | semidirect |
| 20. #124×C173 | C4 | semidirect |
| 97. C173 | #1958 | semidirect |
| 111. #124 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149742 | 2 |
| C2×#19149741 | 2 |
| C4×D173⋊C8 | 2 |
| #26012435 | 2 |
| #124×D173 | 2 |
| #1958 | 173 |