Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
224 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 66 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×D173⋊C16 | C2 | semidirect |
| 2. C2×#19149750 | C2 | semidirect |
| 3. #26012405 | C2 | direct (N × H) |
| 7. D173⋊C16 | C22 | semidirect |
| 10. #19149750 | C22 | semidirect |
| 79. C2×C173 | #359 | semidirect |
| 83. C173 | C2×#359 | semidirect |
| 165. C2 | #26012405 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D173⋊C16 | 2 |
| C2×#19149750 | 2 |
| #26012405 | 2 |
| C2×#19149698 | 2 |
| C2×#359 | 173 |