Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
262 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26011540 | C2 | semidirect |
| 3. #26011514 | C2 | semidirect |
| 6. #26011250 | C2 | semidirect |
| 7. #344×C173 | C2 | semidirect |
| 18. #19149605 | C4 | semidirect |
| 19. #19149605 | C4 | semidirect |
| 97. C173 | #1861 | semidirect |
| 104. #344 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012257 | 2 |
| #26011540 | 2 |
| #26011514 | 2 |
| #26011509 | 2 |
| C2×#19149605 | 2 |
| #26011250 | 2 |
| #344×C173 | 2 |
| #1861 | 173 |