Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
560 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 193 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. #26011383 | C2 | semidirect |
| 4. #26011353 | C2 | semidirect |
| 5. C4⋊C4×Dic173 | C2 | semidirect |
| 6. C4×C4⋊Dic173 | C2 | semidirect |
| 7. #26011338 | C2 | semidirect |
| 8. #382×C173 | C2 | semidirect |
| 11. C4×D692 | C4 | semidirect |
| 97. C173 | #2357 | semidirect |
| 102. #382 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D692 | 2 |
| #26011392 | 2 |
| #26011383 | 2 |
| #26011353 | 2 |
| C4⋊C4×Dic173 | 2 |
| C4×C4⋊Dic173 | 2 |
| #26011338 | 2 |
| #382×C173 | 2 |
| #2357 | 173 |