Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 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 |
|---|---|---|
| 3. #26011869 | C2 | semidirect |
| 4. #26011840 | C2 | semidirect |
| 5. #26011702 | C2 | semidirect |
| 6. #26011701 | C2 | semidirect |
| 7. #26011698 | C2 | semidirect |
| 11. #462×C173 | C2 | semidirect |
| 101. C4×D173 | Q16 | semidirect |
| 135. C173 | #3209 | semidirect |
| 144. #462 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012045 | 2 |
| C4⋊Q8×D173 | 2 |
| #26011869 | 2 |
| #26011840 | 2 |
| #26011702 | 2 |
| #26011701 | 2 |
| #26011698 | 2 |
| #26011648 | 2 |
| #26011645 | 2 |
| #26011543 | 2 |
| #462×C173 | 2 |
| #3209 | 173 |