Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
896 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 896 conjugacy classes of subgroups — too many to draw. Only its 469 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. C173⋊#564 | C2 | direct (N × H) |
| 58. C2×C173 | #564 | semidirect |
| 61. C173 | C2×#564 | semidirect |
| 120. C2 | C173⋊#564 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C173⋊#564 | 2 |
| C2×#19149671 | 2 |
| C2×#19149670 | 2 |
| C2×#19149669 | 2 |
| C2×#125×C173 | 2 |
| C2×#564 | 173 |