Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26011971 | C2 | semidirect |
| 3. #26011835 | C2 | semidirect |
| 4. #26011828 | C2 | semidirect |
| 5. #26011817 | C2 | semidirect |
| 6. #26011806 | C2 | semidirect |
| 7. C2×#19149612 | C2 | semidirect |
| 8. #26011493 | C2 | semidirect |
| 9. #26011485 | C2 | semidirect |
| 10. #26011459 | C2 | semidirect |
| 11. #428×C173 | C2 | semidirect |
| 133. C173 | #3098 | semidirect |
| 141. #428 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012072 | 2 |
| #26011971 | 2 |
| #26011835 | 2 |
| #26011828 | 2 |
| #26011817 | 2 |
| #26011806 | 2 |
| C2×#19149612 | 2 |
| #26011493 | 2 |
| #26011485 | 2 |
| #26011459 | 2 |
| #428×C173 | 2 |
| #3098 | 173 |