Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 9. #19149678 | C4 | semidirect |
| 10. #19149670 | C4 | semidirect |
| 38. C4×Dic173 | Q8 | semidirect |
| 48. C42×C173 | Q8 | semidirect |
| 86. C173 | #1994 | semidirect |
| 135. C42 | Dic346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012044 | 2 |
| #26011514 | 2 |
| C42×Dic173 | 2 |
| #26011252 | 2 |
| #26011251 | 2 |
| #26011250 | 2 |
| #339×C173 | 2 |
| #1994 | 173 |