Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
300 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 18. C4×Dic173 | C8 | semidirect |
| 49. C4×C173 | C4⋊C8 | semidirect |
| 51. Dic173 | C4⋊C8 | semidirect |
| 60. C173 | #1842 | semidirect |
| 115. C4 | #19149746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149746 | 2 |
| C2×C4⋊#13063443 | 2 |
| C42×Dic173 | 2 |
| #1842 | 173 |