Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
400 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 210 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×#19149754 | C2 | semidirect |
| 2. D173⋊M32 | C2 | direct (N × H) |
| 3. C2×#19149753 | C2 | semidirect |
| 4. C2×D173⋊C16 | C2 | semidirect |
| 6. #19149754 | C22 | semidirect |
| 7. #19149753 | C22 | semidirect |
| 8. D173⋊C16 | C22 | semidirect |
| 9. C2×#14583829 | C22 | semidirect |
| 19. #14583829 | C23 | semidirect |
| 70. C2×D173 | M32 | semidirect |
| 79. C2×C173 | C2×M32 | semidirect |
| 82. D173 | C2×M32 | semidirect |
| 83. C173 | C22×M32 | semidirect |
| 165. C2 | D173⋊M32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149754 | 2 |
| D173⋊M32 | 2 |
| C2×#19149753 | 2 |
| C2×D173⋊C16 | 2 |
| C22×C8×D173 | 2 |
| C22×M32 | 173 |