Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
512 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 189 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. #26011378 | C2 | semidirect |
| 3. #26011372 | C2 | semidirect |
| 11. C2×#14583805 | C4 | semidirect |
| 90. C173 | #2313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583805 | 2 |
| #26011378 | 2 |
| #26011372 | 2 |
| #26011352 | 2 |
| #26011351 | 2 |
| C22⋊C4×Dic173 | 2 |
| #380×C173 | 2 |
| #2313 | 173 |