Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
296 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 13. #19149608 | C4 | semidirect |
| 16. C8×Dic173 | C4 | semidirect |
| 30. #14583805 | C8 | semidirect |
| 53. #13063436 | C4⋊C4 | semidirect |
| 78. Dic173 | C4×C8 | semidirect |
| 84. C173 | C8×C4⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149608 | 2 |
| C2×C4×#13063436 | 2 |
| C2×C8×Dic173 | 2 |
| C4×#14583805 | 2 |
| #26011245 | 2 |
| #336×C173 | 2 |
| C8×C4⋊C4 | 173 |