Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
240 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 3. #26011240 | C2 | semidirect |
| 70. C173 | #1548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011544 | 2 |
| #26011515 | 2 |
| #26011240 | 2 |
| C2×C4⋊Q8×C173 | 2 |
| #1548 | 173 |