Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 85 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. #19149678 | C4 | semidirect |
| 11. #19149670 | C4 | semidirect |
| 12. #19149670 | C4 | semidirect |
| 33. #14583810 | Q8 | semidirect |
| 55. M16×C173 | Q8 | semidirect |
| 114. C173 | #1986 | semidirect |
| 152. M16 | Dic346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012044 | 2 |
| M16×Dic173 | 2 |
| C4×#14583805 | 2 |
| #26011252 | 2 |
| #26011251 | 2 |
| #26011250 | 2 |
| #339×C173 | 2 |
| #1986 | 173 |