Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
370 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 370 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. #26012027 | C2 | semidirect |
| 2. #26011891 | C2 | semidirect |
| 3. #26011876 | C2 | semidirect |
| 4. #26011847 | C2 | semidirect |
| 6. #26011739 | C2 | semidirect |
| 7. #26011602 | C2 | semidirect |
| 8. #26011598 | C2 | semidirect |
| 9. #26011594 | C2 | semidirect |
| 10. M16×Dic173 | C2 | semidirect |
| 11. #470×C173 | C2 | semidirect |
| 109. C173 | #3183 | semidirect |
| 115. #470 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012027 | 2 |
| #26011891 | 2 |
| #26011876 | 2 |
| #26011847 | 2 |
| #26011744 | 2 |
| #26011739 | 2 |
| #26011602 | 2 |
| #26011598 | 2 |
| #26011594 | 2 |
| M16×Dic173 | 2 |
| #470×C173 | 2 |
| #3183 | 173 |