Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
338 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26011890 | C2 | semidirect |
| 4. #26011870 | C2 | semidirect |
| 5. #26011860 | C2 | semidirect |
| 8. #26011595 | C2 | semidirect |
| 9. #26011583 | C2 | semidirect |
| 11. #491×C173 | C2 | semidirect |
| 102. C173 | #3177 | semidirect |
| 109. #491 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012104 | 2 |
| #26012102 | 2 |
| #26011890 | 2 |
| #26011870 | 2 |
| #26011860 | 2 |
| #26011748 | 2 |
| #26011731 | 2 |
| #26011595 | 2 |
| #26011583 | 2 |
| #26011448 | 2 |
| #491×C173 | 2 |
| #3177 | 173 |