Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
348 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. #26012219 | C2 | semidirect |
| 3. #26011846 | C2 | semidirect |
| 5. #26011792 | C2 | semidirect |
| 6. #26011777 | C2 | semidirect |
| 7. #26011714 | C2 | semidirect |
| 9. C4×Dic692 | C2 | semidirect |
| 10. C4×#14583815 | C2 | semidirect |
| 11. C8×Q8×C173 | C2 | semidirect |
| 117. C173 | #3365 | semidirect |
| 127. C8×Q8 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012226 | 2 |
| #26012219 | 2 |
| #26011846 | 2 |
| #26011838 | 2 |
| #26011792 | 2 |
| #26011777 | 2 |
| #26011714 | 2 |
| #26011692 | 2 |
| C4×Dic692 | 2 |
| C4×#14583815 | 2 |
| C8×Q8×C173 | 2 |
| #3365 | 173 |