Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
220 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. C2×#19149619 | C2 | semidirect |
| 3. #26011276 | C2 | semidirect |
| 4. C2×M32×C173 | C2 | semidirect |
| 15. C2×#14583801 | C22 | semidirect |
| 18. M32×C173 | C22 | semidirect |
| 82. C173 | #2117 | semidirect |
| 86. C2×M32 | D173 | semidirect |
| 100. M32 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149685 | 2 |
| C2×#19149619 | 2 |
| #26011276 | 2 |
| C2×M32×C173 | 2 |
| #2117 | 173 |