Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26012041 | C2 | semidirect |
| 2. #26011901 | C2 | semidirect |
| 3. #26011881 | C2 | semidirect |
| 4. #26011857 | C2 | semidirect |
| 5. #26011850 | C2 | semidirect |
| 6. #26011742 | C2 | semidirect |
| 7. #26011739 | C2 | semidirect |
| 8. C4×#14583813 | C2 | semidirect |
| 9. C4×#14583811 | C2 | semidirect |
| 10. C4×#14583810 | C2 | semidirect |
| 11. #529×C173 | C2 | semidirect |
| 92. #13063436 | #41 | semidirect |
| 137. C173 | #3171 | semidirect |
| 140. #529 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012041 | 2 |
| #26011901 | 2 |
| #26011881 | 2 |
| #26011857 | 2 |
| #26011850 | 2 |
| #26011742 | 2 |
| #26011739 | 2 |
| C4×#14583813 | 2 |
| C4×#14583811 | 2 |
| C4×#14583810 | 2 |
| #529×C173 | 2 |
| #3171 | 173 |