Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
156 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 36. Q8×C173 | Q16 | semidirect |
| 57. C173 | #1670 | semidirect |
| 92. Q8 | Dic692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011871 | 2 |
| #26011776 | 2 |
| #26011244 | 2 |
| #26011238 | 2 |
| C8×Q8×C173 | 2 |
| #1670 | 173 |