Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
160 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 78 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. #26012384 | C2 | semidirect |
| 3. #26012383 | C2 | semidirect |
| 5. #19149754 | C4 | semidirect |
| 7. D173⋊C16 | C4 | semidirect |
| 51. C173 | #2110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊M32 | 2 |
| #26012384 | 2 |
| #26012383 | 2 |
| #26011445 | 2 |
| #2110 | 173 |