Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
572 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 572 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×#19149701 | C2 | semidirect |
| 2. C2×#19149699 | C2 | semidirect |
| 3. #26012037 | C2 | semidirect |
| 4. #26011876 | C2 | semidirect |
| 5. #26011874 | C2 | semidirect |
| 6. #26011872 | C2 | semidirect |
| 7. #26011869 | C2 | semidirect |
| 8. #26011866 | C2 | semidirect |
| 9. #26011862 | C2 | semidirect |
| 10. C2×C8×Dic173 | C2 | semidirect |
| 11. C2×#135×C173 | C2 | semidirect |
| 55. C2×#13063436 | D4 | semidirect |
| 74. C2×C8×C173 | D4 | semidirect |
| 119. Dic173 | #135 | semidirect |
| 125. C173 | #3147 | semidirect |
| 129. C2×#135 | D173 | semidirect |
| 194. C2×C8 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149701 | 2 |
| C2×#19149699 | 2 |
| #26012037 | 2 |
| #26011876 | 2 |
| #26011874 | 2 |
| #26011872 | 2 |
| #26011869 | 2 |
| #26011866 | 2 |
| #26011862 | 2 |
| C2×C8×Dic173 | 2 |
| C2×#135×C173 | 2 |
| #3147 | 173 |