Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26012046 | C2 | semidirect |
| 3. #26011835 | C2 | semidirect |
| 4. #26011783 | C2 | semidirect |
| 5. #26011702 | C2 | semidirect |
| 6. #26011696 | C2 | semidirect |
| 8. #26011597 | C2 | semidirect |
| 9. #26011588 | C2 | semidirect |
| 10. #26011547 | C2 | semidirect |
| 11. #476×C173 | C2 | semidirect |
| 136. C173 | #3116 | semidirect |
| 142. #476 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012046 | 2 |
| C4×#14583825 | 2 |
| #26011835 | 2 |
| #26011783 | 2 |
| #26011702 | 2 |
| #26011696 | 2 |
| #26011654 | 2 |
| #26011597 | 2 |
| #26011588 | 2 |
| #26011547 | 2 |
| #476×C173 | 2 |
| #3116 | 173 |