Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 2. #26012220 | C2 | semidirect |
| 3. #26011847 | C2 | semidirect |
| 5. #26011794 | C2 | semidirect |
| 6. #26011776 | C2 | semidirect |
| 7. #26011715 | C2 | semidirect |
| 9. C8×Dic346 | C2 | semidirect |
| 10. #26011576 | C2 | semidirect |
| 11. C4×Q16×C173 | C2 | semidirect |
| 117. C173 | #3365 | semidirect |
| 128. C4×Q16 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012226 | 2 |
| #26012220 | 2 |
| #26011847 | 2 |
| #26011838 | 2 |
| #26011794 | 2 |
| #26011776 | 2 |
| #26011715 | 2 |
| #26011691 | 2 |
| C8×Dic346 | 2 |
| #26011576 | 2 |
| C4×Q16×C173 | 2 |
| #3365 | 173 |