Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
500 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 217 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 |
| 39. C4×Dic173 | Q8 | semidirect |
| 87. C173 | #2295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic346 | 2 |
| #26011396 | 2 |
| #26011387 | 2 |
| #26011373 | 2 |
| C4×#14583805 | 2 |
| #26011337 | 2 |
| C42×Dic173 | 2 |
| C4×C4⋊C4×C173 | 2 |
| #2295 | 173 |