Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
774 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 206 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×#19149767 | C2 | semidirect |
| 2. #26012466 | C2 | semidirect |
| 3. #26012462 | C2 | semidirect |
| 4. D173⋊(C22⋊C8) | C2 | semidirect |
| 7. C2×#14583836 | C22 | semidirect |
| 8. C2×D173⋊C8 | C22 | semidirect |
| 9. #19149736 | C22 | semidirect |
| 10. #19149736 | C22 | semidirect |
| 69. C22×C173 | #131 | semidirect |
| 88. C173 | #2880 | semidirect |
| 165. C22 | #19149767 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149767 | 2 |
| #26012466 | 2 |
| #26012462 | 2 |
| D173⋊(C22⋊C8) | 2 |
| C22×#14583827 | 2 |
| #2880 | 173 |