Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 3. #26011783 | C2 | semidirect |
| 5. Q8⋊#13063436 | C2 | semidirect |
| 6. #26011221 | C2 | semidirect |
| 7. #477×C173 | C2 | semidirect |
| 89. C173 | #1630 | semidirect |
| 94. #477 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012226 | 2 |
| #26011865 | 2 |
| #26011783 | 2 |
| #26011234 | 2 |
| Q8⋊#13063436 | 2 |
| #26011221 | 2 |
| #477×C173 | 2 |
| #1630 | 173 |