Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
154 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 49. C4×C173 | Q32 | semidirect |
| 56. C173 | #2209 | semidirect |
| 107. C4 | #19149625 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149625 | 2 |
| #26011871 | 2 |
| C4⋊#14583801 | 2 |
| #26011294 | 2 |
| C4×Q16×C173 | 2 |
| #2209 | 173 |