Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. #26012046 | C2 | semidirect |
| 3. #26011858 | C2 | semidirect |
| 4. #26011854 | C2 | semidirect |
| 5. #26011853 | C2 | semidirect |
| 6. #26011851 | C2 | semidirect |
| 7. #26011850 | C2 | semidirect |
| 8. #26011486 | C2 | semidirect |
| 9. #26011484 | C2 | semidirect |
| 10. #97×D173 | C2 | semidirect |
| 11. #489×C173 | C2 | semidirect |
| 137. C173 | #3135 | semidirect |
| 146. #489 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012046 | 2 |
| #26012040 | 2 |
| #26011858 | 2 |
| #26011854 | 2 |
| #26011853 | 2 |
| #26011851 | 2 |
| #26011850 | 2 |
| #26011486 | 2 |
| #26011484 | 2 |
| #97×D173 | 2 |
| #489×C173 | 2 |
| #3135 | 173 |