Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
408 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26012207 | C2 | semidirect |
| 2. #26012163 | C2 | semidirect |
| 3. #26011839 | C2 | semidirect |
| 4. #26011818 | C2 | semidirect |
| 5. #26011728 | C2 | semidirect |
| 6. #26011687 | C2 | semidirect |
| 7. #26011639 | C2 | semidirect |
| 8. C4×#14583813 | C2 | semidirect |
| 9. #26011556 | C2 | semidirect |
| 10. #26011486 | C2 | semidirect |
| 11. #477×C173 | C2 | semidirect |
| 132. C173 | #3305 | semidirect |
| 138. #477 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012207 | 2 |
| #26012163 | 2 |
| #26011839 | 2 |
| #26011818 | 2 |
| #26011728 | 2 |
| #26011687 | 2 |
| #26011639 | 2 |
| C4×#14583813 | 2 |
| #26011556 | 2 |
| #26011486 | 2 |
| #477×C173 | 2 |
| #3305 | 173 |