Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
696 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 189 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×#19149667 | C2 | semidirect |
| 2. C2×#19149658 | C2 | semidirect |
| 4. #26011397 | C2 | semidirect |
| 5. #26011393 | C2 | semidirect |
| 6. #26011382 | C2 | semidirect |
| 7. #26011370 | C2 | semidirect |
| 8. #26011357 | C2 | semidirect |
| 9. C22×C42×C173 | C2 | semidirect |
| 63. C42×C173 | D4 | semidirect |
| 103. C22×C173 | #124 | semidirect |
| 128. C173 | #2850 | semidirect |
| 133. C22×C42 | D173 | semidirect |
| 192. C42 | C22⋊D173 | semidirect |
| 237. C22 | #19149667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149667 | 2 |
| C2×#19149658 | 2 |
| C2×#19149653 | 2 |
| #26011397 | 2 |
| #26011393 | 2 |
| #26011382 | 2 |
| #26011370 | 2 |
| #26011357 | 2 |
| C22×C42×C173 | 2 |
| #2850 | 173 |