Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
436 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 98 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×#19149741 | C2 | semidirect |
| 2. C4×D173⋊C8 | C2 | semidirect |
| 3. #26012437 | C2 | semidirect |
| 12. #19149676 | C4 | semidirect |
| 14. #19149675 | C4 | semidirect |
| 16. #127×C173 | C4 | semidirect |
| 19. D173⋊C8 | D4 | semidirect |
| 76. C4×C173 | #102 | semidirect |
| 78. Dic173 | #102 | semidirect |
| 87. C173 | #1957 | semidirect |
| 99. #127 | #10621924 | semidirect |
| 166. C4 | #19149741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149741 | 2 |
| C4×D173⋊C8 | 2 |
| #26012437 | 2 |
| #127×D173 | 2 |
| #1957 | 173 |