Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
400 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 129 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. #26011847 | C2 | semidirect |
| 4. #26011844 | C2 | semidirect |
| 5. #26011840 | C2 | semidirect |
| 6. #26011836 | C2 | semidirect |
| 7. #26011488 | C2 | semidirect |
| 8. #26011487 | C2 | semidirect |
| 9. #26011485 | C2 | semidirect |
| 10. C2×C8×Dic173 | C2 | semidirect |
| 11. #416×C173 | C2 | semidirect |
| 125. C173 | #3131 | 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 |
| #26011847 | 2 |
| #26011844 | 2 |
| #26011840 | 2 |
| #26011836 | 2 |
| #26011488 | 2 |
| #26011487 | 2 |
| #26011485 | 2 |
| C2×C8×Dic173 | 2 |
| #416×C173 | 2 |
| #3131 | 173 |