Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
164 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 17. Dic692 | C8 | direct (N × H) |
| 40. C8×C173 | Q16 | semidirect |
| 52. C173 | C8×Q16 | semidirect |
| 93. C8 | Dic692 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic346 | 2 |
| C4×Dic692 | 2 |
| #26011244 | 2 |
| #26011223 | 2 |
| C82×C173 | 2 |
| C8×Q16 | 173 |