Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
416 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 173 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. #26011783 | C2 | direct (N × H) |
| 25. C2×Dic346 | Q8 | semidirect |
| 48. Dic346 | C2×Q8 | semidirect |
| 78. C2×C173 | #477 | semidirect |
| 82. C173 | C2×#477 | semidirect |
| 161. C2 | #26011783 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic346 | 2 |
| #26011783 | 2 |
| C2×#19149612 | 2 |
| C2×C4⋊#13063436 | 2 |
| C2×#19149602 | 2 |
| C2×C4⋊Q8×C173 | 2 |
| C2×#477 | 173 |