Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26012114 | C2 | semidirect |
| 2. #26011888 | C2 | semidirect |
| 3. #26011876 | C2 | semidirect |
| 4. #26011852 | C2 | semidirect |
| 6. #26011722 | C2 | semidirect |
| 7. #26011602 | C2 | semidirect |
| 8. #26011598 | C2 | semidirect |
| 9. #26011576 | C2 | semidirect |
| 10. #26011449 | C2 | semidirect |
| 11. #470×C173 | C2 | semidirect |
| 109. C173 | #3173 | semidirect |
| 115. #470 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012114 | 2 |
| #26011888 | 2 |
| #26011876 | 2 |
| #26011852 | 2 |
| #26011744 | 2 |
| #26011722 | 2 |
| #26011602 | 2 |
| #26011598 | 2 |
| #26011576 | 2 |
| #26011449 | 2 |
| #470×C173 | 2 |
| #3173 | 173 |