Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
236 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 74 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. D173⋊M32 | C2 | semidirect |
| 2. #26012388 | C2 | semidirect |
| 3. #26012387 | C2 | semidirect |
| 6. #19149753 | C22 | semidirect |
| 90. D173 | #349 | semidirect |
| 91. C173 | C2×#349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊M32 | 2 |
| #26012388 | 2 |
| #26012387 | 2 |
| C2×M16×D173 | 2 |
| C2×#349 | 173 |