Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
196 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 100 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. #26012378 | C2 | semidirect |
| 4. C16×#10621924 | C2 | semidirect |
| 8. #19149754 | C4 | semidirect |
| 9. #19149753 | C4 | semidirect |
| 16. #19149619 | C4 | semidirect |
| 17. #19149618 | C4 | semidirect |
| 19. M32×C173 | C4 | semidirect |
| 28. #14583829 | C2×C4 | semidirect |
| 35. #14583801 | C2×C4 | semidirect |
| 37. C16×C173 | C2×C4 | semidirect |
| 59. #10621924 | M32 | direct (N × H) |
| 68. C173 | C4×M32 | semidirect |
| 82. M32 | #10621924 | direct (N × H) |
| 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×C8×#10621924 | 2 |
| #26012378 | 2 |
| C16×#10621924 | 2 |
| M32×D173 | 2 |
| C4×M32 | 173 |