Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
552 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 1. C2×#19149712 | C2 | semidirect |
| 2. C2×#19149710 | C2 | semidirect |
| 3. C2×#19149709 | C2 | semidirect |
| 5. C2×#19149677 | C2 | semidirect |
| 6. #26011884 | C2 | semidirect |
| 7. #26011882 | C2 | semidirect |
| 8. #26011869 | C2 | semidirect |
| 9. #26011862 | C2 | semidirect |
| 10. M16×Dic173 | C2 | semidirect |
| 11. C2×#137×C173 | C2 | semidirect |
| 62. #14583810 | D4 | semidirect |
| 86. M16×C173 | D4 | semidirect |
| 140. Dic173 | #137 | semidirect |
| 146. C173 | #3152 | semidirect |
| 151. C2×#137 | D173 | semidirect |
| 224. M16 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149712 | 2 |
| C2×#19149710 | 2 |
| C2×#19149709 | 2 |
| #26012037 | 2 |
| C2×#19149677 | 2 |
| #26011884 | 2 |
| #26011882 | 2 |
| #26011869 | 2 |
| #26011862 | 2 |
| M16×Dic173 | 2 |
| C2×#137×C173 | 2 |
| #3152 | 173 |