Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19149709 | C2 | semidirect |
| 2. C2×#19149685 | C2 | semidirect |
| 4. #26012067 | C2 | semidirect |
| 5. #26011748 | C2 | semidirect |
| 6. #26011736 | C2 | semidirect |
| 7. #26011731 | C2 | semidirect |
| 8. #26011719 | C2 | semidirect |
| 9. #26011534 | C2 | semidirect |
| 10. C2×#19149604 | C2 | semidirect |
| 11. #416×C173 | C2 | semidirect |
| 58. #14583810 | D4 | semidirect |
| 143. C173 | #3063 | semidirect |
| 154. #416 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149709 | 2 |
| C2×#19149685 | 2 |
| #26012069 | 2 |
| #26012067 | 2 |
| #26011748 | 2 |
| #26011736 | 2 |
| #26011731 | 2 |
| #26011719 | 2 |
| #26011534 | 2 |
| C2×#19149604 | 2 |
| #416×C173 | 2 |
| #3063 | 173 |