Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
764 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 202 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⋊M16 | C2 | semidirect |
| 2. #26012466 | C2 | semidirect |
| 3. #26012463 | C2 | semidirect |
| 5. C2×#14583836 | C22 | semidirect |
| 8. C2×D173⋊C8 | C22 | semidirect |
| 9. #19149736 | C22 | semidirect |
| 83. C173 | #2879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D173⋊M16 | 2 |
| #26012466 | 2 |
| #26012463 | 2 |
| C22×#14583827 | 2 |
| #2879 | 173 |