Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
160 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 5. C2×#14583829 | C4 | semidirect |
| 24. C2×Dic173 | C16 | semidirect |
| 50. C173 | #1374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583829 | 2 |
| C2×C8×Dic173 | 2 |
| #1374 | 173 |