Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
564 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19149598 | C2 | semidirect |
| 49. C22×C173 | #101 | semidirect |
| 59. C173 | #1784 | semidirect |
| 109. C22 | #19149598 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149598 | 2 |
| #26011455 | 2 |
| C23×Q8×C173 | 2 |
| #1784 | 173 |