Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
264 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 1. C2×#19149615 | C2 | semidirect |
| 2. C2×#19149613 | C2 | semidirect |
| 4. #26011259 | C2 | semidirect |
| 15. #131×C173 | C4 | semidirect |
| 87. C173 | #1816 | semidirect |
| 96. #131 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149615 | 2 |
| C2×#19149613 | 2 |
| #26011492 | 2 |
| #26011259 | 2 |
| C2×#131×C173 | 2 |
| #1816 | 173 |