Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 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×#19149699 | C2 | semidirect |
| 2. C2×#19149687 | C2 | semidirect |
| 3. #26012072 | C2 | semidirect |
| 4. #26012069 | C2 | semidirect |
| 5. #26011740 | C2 | semidirect |
| 6. #26011736 | C2 | semidirect |
| 7. #26011731 | C2 | semidirect |
| 8. #26011726 | C2 | semidirect |
| 9. C2×#19149612 | C2 | semidirect |
| 10. #26011493 | C2 | semidirect |
| 11. #417×C173 | C2 | semidirect |
| 63. C2×#13063436 | D4 | semidirect |
| 152. C173 | #3061 | semidirect |
| 164. #417 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149699 | 2 |
| C2×#19149687 | 2 |
| #26012072 | 2 |
| #26012069 | 2 |
| #26011740 | 2 |
| #26011736 | 2 |
| #26011731 | 2 |
| #26011726 | 2 |
| C2×#19149612 | 2 |
| #26011493 | 2 |
| #417×C173 | 2 |
| #3061 | 173 |