Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×Q8×Dic173 | C2 | semidirect |
| 3. #26011824 | C2 | semidirect |
| 5. #26011796 | C2 | semidirect |
| 6. #26011715 | C2 | semidirect |
| 8. #26011598 | C2 | semidirect |
| 9. #26011594 | C2 | semidirect |
| 10. #26011545 | C2 | semidirect |
| 11. #451×C173 | C2 | semidirect |
| 131. C173 | #3117 | semidirect |
| 139. #451 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012027 | 2 |
| C2×Q8×Dic173 | 2 |
| #26011824 | 2 |
| #26011810 | 2 |
| #26011796 | 2 |
| #26011715 | 2 |
| #26011630 | 2 |
| #26011598 | 2 |
| #26011594 | 2 |
| #26011545 | 2 |
| #451×C173 | 2 |
| #3117 | 173 |