Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
428 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 88 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×#19149741 | C2 | semidirect |
| 3. C4×C4⋊#10621924 | C2 | semidirect |
| 15. #19149676 | C4 | semidirect |
| 18. #19149675 | C4 | semidirect |
| 20. #127×C173 | C4 | semidirect |
| 25. C4⋊#10621924 | D4 | semidirect |
| 96. C4×C173 | #102 | semidirect |
| 99. Dic173 | #102 | semidirect |
| 109. C173 | #1982 | semidirect |
| 123. #127 | #10621924 | semidirect |
| 210. C4 | #19149741 | 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×#19149741 | 2 |
| C4×C4⋊#10621924 | 2 |
| #127×D173 | 2 |
| #1982 | 173 |