Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
380 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 5. #26011774 | C2 | semidirect |
| 6. #26011699 | C2 | semidirect |
| 8. #26011598 | C2 | semidirect |
| 9. #26011595 | C2 | semidirect |
| 127. C173 | #3113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012043 | 2 |
| C2×Q8×Dic173 | 2 |
| #26011822 | 2 |
| #26011819 | 2 |
| #26011774 | 2 |
| #26011699 | 2 |
| #26011647 | 2 |
| #26011598 | 2 |
| #26011595 | 2 |
| #26011545 | 2 |
| #451×C173 | 2 |
| #3113 | 173 |