Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
260 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 21. #14583810 | Q8 | semidirect |
| 72. C173 | #1997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011515 | 2 |
| C4×#14583810 | 2 |
| #26011260 | 2 |
| C2×C4⋊Q8×C173 | 2 |
| #1997 | 173 |