Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
752 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 181 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×#19149677 | C2 | semidirect |
| 3. C2×#19149668 | C2 | semidirect |
| 4. C2×#19149667 | C2 | semidirect |
| 5. C2×#19149666 | C2 | semidirect |
| 6. #26011391 | C2 | semidirect |
| 7. C42×Dic173 | C2 | semidirect |
| 8. C2×#124×C173 | C2 | semidirect |
| 47. C4×Dic173 | D4 | semidirect |
| 59. C42×C173 | D4 | semidirect |
| 106. Dic173 | #124 | semidirect |
| 113. C173 | #2858 | semidirect |
| 120. C2×#124 | D173 | semidirect |
| 173. C42 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149677 | 2 |
| C2×#19149675 | 2 |
| C2×#19149668 | 2 |
| C2×#19149667 | 2 |
| C2×#19149666 | 2 |
| #26011391 | 2 |
| C42×Dic173 | 2 |
| C2×#124×C173 | 2 |
| #2858 | 173 |