Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
140 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 6. #19149748 | C4 | semidirect |
| 9. #19149747 | C4 | semidirect |
| 11. #19149619 | C4 | semidirect |
| 14. M32×C173 | C4 | semidirect |
| 58. C173 | #1386 | semidirect |
| 68. M32 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012501 | 2 |
| C2×#19149747 | 2 |
| M32×D173 | 2 |
| #1386 | 173 |