Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
168 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26011312 | C2 | direct (N × H) |
| 51. C2×C173 | #364 | semidirect |
| 53. C173 | C2×#364 | semidirect |
| 105. C2 | #26011312 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149619 | 2 |
| #26011312 | 2 |
| C2×C4×C8×C173 | 2 |
| C2×#364 | 173 |