Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
280 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 10. #19149610 | C4 | direct (N × H) |
| 11. C4×#13063436 | C4 | semidirect |
| 38. #13063436 | C42 | semidirect |
| 59. C4×C173 | #106 | semidirect |
| 69. C173 | C4×#106 | semidirect |
| 130. C4 | #19149610 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149610 | 2 |
| C2×C4×#13063436 | 2 |
| C4×C4⋊Dic173 | 2 |
| #26011253 | 2 |
| C4×C4⋊C4×C173 | 2 |
| C4×#106 | 173 |