Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
344 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 344 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. D173⋊(C4⋊C8) | C2 | semidirect |
| 2. C2×#19149742 | C2 | semidirect |
| 4. C4×C4⋊#10621924 | C2 | semidirect |
| 16. #19149668 | C4 | semidirect |
| 17. #19149667 | C4 | semidirect |
| 18. #19149666 | C4 | semidirect |
| 24. #124×C173 | C4 | semidirect |
| 122. C173 | #1983 | semidirect |
| 137. #124 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊(C4⋊C8) | 2 |
| C2×#19149742 | 2 |
| C2×#19149741 | 2 |
| C4×C4⋊#10621924 | 2 |
| #124×D173 | 2 |
| #1983 | 173 |