Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. #26011833 | C2 | semidirect |
| 4. #26011827 | C2 | semidirect |
| 5. #26011822 | C2 | semidirect |
| 6. #26011533 | C2 | semidirect |
| 7. #26011501 | C2 | semidirect |
| 25. #19149613 | C22 | semidirect |
| 26. #19149611 | C22 | semidirect |
| 27. #19149604 | C22 | semidirect |
| 28. #19149604 | C22 | semidirect |
| 116. C173 | #3095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149658 | 2 |
| C2×#19149638 | 2 |
| #26011833 | 2 |
| #26011827 | 2 |
| #26011822 | 2 |
| #26011533 | 2 |
| #26011501 | 2 |
| #407×C173 | 2 |
| #3095 | 173 |