Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
300 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 8. #19149679 | C4 | semidirect |
| 22. C2×#13063436 | Q8 | semidirect |
| 74. C173 | #1990 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149679 | 2 |
| C2×C4×#13063436 | 2 |
| #26011253 | 2 |
| #384×C173 | 2 |
| #1990 | 173 |