Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
504 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 177 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 |
|---|---|---|
| 37. C4×Dic173 | Q8 | semidirect |
| 87. C173 | #2399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic346 | 2 |
| #26011422 | 2 |
| #26011421 | 2 |
| #26011411 | 2 |
| #26011410 | 2 |
| C4×#14583805 | 2 |
| #26011337 | 2 |
| C2×C4×Q8×C173 | 2 |
| #2399 | 173 |