Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
150 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 11. #19149625 | C4 | semidirect |
| 59. Dic173 | Q32 | semidirect |
| 63. C173 | C4×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149625 | 2 |
| Q16×Dic173 | 2 |
| #26011585 | 2 |
| #26011316 | 2 |
| #26011296 | 2 |
| C16×Dic173 | 2 |
| #358×C173 | 2 |
| C4×Q32 | 173 |