Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
564 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 177 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. #26011398 | C2 | semidirect |
| 3. #26011387 | C2 | semidirect |
| 4. #26011372 | C2 | semidirect |
| 31. C22×Dic173 | Q8 | semidirect |
| 102. C173 | #2855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic173 | 2 |
| #26011398 | 2 |
| #26011387 | 2 |
| #26011372 | 2 |
| #26011363 | 2 |
| #26011352 | 2 |
| #26011351 | 2 |
| C2×C22⋊Q8×C173 | 2 |
| #2855 | 173 |