Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
278 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. C2×#19149615 | C2 | semidirect |
| 3. C2×#19149614 | C2 | semidirect |
| 6. #26011255 | C2 | semidirect |
| 7. #341×C173 | C2 | semidirect |
| 99. C2×D173 | #108 | semidirect |
| 113. C173 | #1855 | semidirect |
| 121. #341 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D173 | 2 |
| C2×#19149615 | 2 |
| C2×#19149614 | 2 |
| #26011454 | 2 |
| C2×#19149591 | 2 |
| #26011255 | 2 |
| #341×C173 | 2 |
| #1855 | 173 |