Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 1. #26012044 | C2 | semidirect |
| 3. #26011858 | C2 | semidirect |
| 4. #26011854 | C2 | semidirect |
| 5. #26011852 | C2 | semidirect |
| 6. #26011849 | C2 | semidirect |
| 7. #26011488 | C2 | semidirect |
| 8. #26011487 | C2 | semidirect |
| 9. #26011485 | C2 | semidirect |
| 10. C2×#19149589 | C2 | semidirect |
| 11. #416×C173 | C2 | semidirect |
| 125. C173 | #3135 | semidirect |
| 136. #416 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012044 | 2 |
| #26012037 | 2 |
| #26011858 | 2 |
| #26011854 | 2 |
| #26011852 | 2 |
| #26011849 | 2 |
| #26011488 | 2 |
| #26011487 | 2 |
| #26011485 | 2 |
| C2×#19149589 | 2 |
| #416×C173 | 2 |
| #3135 | 173 |