Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
168 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 80 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. #26012382 | C2 | semidirect |
| 4. #26012381 | C2 | semidirect |
| 9. #19149753 | C4 | semidirect |
| 10. D173⋊C16 | C4 | semidirect |
| 16. #19149619 | C4 | semidirect |
| 18. C16×D173 | C4 | semidirect |
| 19. M32×C173 | C4 | semidirect |
| 28. #14583829 | C2×C4 | semidirect |
| 35. #14583801 | C2×C4 | semidirect |
| 37. C16×C173 | C2×C4 | semidirect |
| 67. D173 | #347 | semidirect |
| 68. C173 | C2×#347 | semidirect |
| 82. M32 | #10621924 | semidirect |
| 106. C16 | C2×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊M32 | 2 |
| C2×#19149733 | 2 |
| #26012382 | 2 |
| #26012381 | 2 |
| M32×D173 | 2 |
| C2×#347 | 173 |