Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
292 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 292 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×#19149605 | C2 | semidirect |
| 3. #26011459 | C2 | semidirect |
| 4. C2×#19149589 | C2 | semidirect |
| 5. C2×#108×C173 | C2 | semidirect |
| 9. C2×Dic692 | C4 | semidirect |
| 10. C2×#14583815 | C4 | semidirect |
| 11. C2×D1384 | C4 | semidirect |
| 85. C173 | #1975 | semidirect |
| 88. C2×#108 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149701 | 2 |
| C2×#19149605 | 2 |
| #26011459 | 2 |
| C2×#19149589 | 2 |
| C2×#108×C173 | 2 |
| #1975 | 173 |