Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
500 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 10. C4×Dic346 | C4 | semidirect |
| 46. C42×C173 | Q8 | semidirect |
| 87. C173 | #2295 | semidirect |
| 134. C42 | Dic346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic346 | 2 |
| #26011397 | 2 |
| #26011389 | 2 |
| #26011375 | 2 |
| C4×#14583805 | 2 |
| C4×C4⋊Dic173 | 2 |
| #26011337 | 2 |
| C43×C173 | 2 |
| #2295 | 173 |