Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
160 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 53 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×#19149624 | C2 | semidirect |
| 2. #26011732 | C2 | semidirect |
| 4. #26011317 | C2 | semidirect |
| 5. #26011296 | C2 | semidirect |
| 6. #26011293 | C2 | semidirect |
| 7. C2×M32×C173 | C2 | semidirect |
| 39. C16×C173 | D4 | semidirect |
| 75. C173 | #2220 | semidirect |
| 78. C2×M32 | D173 | semidirect |
| 115. C16 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149624 | 2 |
| #26011732 | 2 |
| #26011727 | 2 |
| #26011317 | 2 |
| #26011296 | 2 |
| #26011293 | 2 |
| C2×M32×C173 | 2 |
| #2220 | 173 |