Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #26011831 | C2 | semidirect |
| 4. #26011830 | C2 | semidirect |
| 5. #26011825 | C2 | semidirect |
| 6. #26011820 | C2 | semidirect |
| 7. #26011533 | C2 | semidirect |
| 8. #26011527 | C2 | semidirect |
| 9. C2×#19149603 | C2 | semidirect |
| 11. #419×C173 | C2 | semidirect |
| 126. C173 | #3097 | semidirect |
| 136. #419 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012065 | 2 |
| #26011971 | 2 |
| #26011831 | 2 |
| #26011830 | 2 |
| #26011825 | 2 |
| #26011820 | 2 |
| #26011533 | 2 |
| #26011527 | 2 |
| C2×#19149603 | 2 |
| #26011459 | 2 |
| #419×C173 | 2 |
| #3097 | 173 |