Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
908 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 285 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 |
|---|---|---|
| 2. #26011410 | C2 | direct (N × H) |
| 16. C22×Dic173 | Q8 | semidirect |
| 31. C2×Dic173 | C2×Q8 | semidirect |
| 49. C2×C173 | #395 | semidirect |
| 53. C173 | C2×#395 | semidirect |
| 103. C2 | #26011410 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583805 | 2 |
| #26011410 | 2 |
| C2×#19149586 | 2 |
| C23×Q8×C173 | 2 |
| C2×#395 | 173 |