Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
598 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 87 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×C22⋊C4×D173 | C2 | semidirect |
| 3. C2×#19149594 | C2 | semidirect |
| 4. #26011346 | C2 | semidirect |
| 5. #26011257 | C2 | semidirect |
| 6. #26011257 | C2 | semidirect |
| 7. C2×#99×C173 | C2 | semidirect |
| 9. C22×C22⋊D173 | C4 | semidirect |
| 19. C2×#14583803 | C4 | semidirect |
| 41. C22×Dic173 | C2×C4 | semidirect |
| 49. C22⋊Dic173 | D4 | semidirect |
| 54. C24×C173 | C2×C4 | semidirect |
| 64. C22×C4×C173 | C2×C4 | semidirect |
| 68. C22⋊C4×C173 | D4 | semidirect |
| 152. C2×D173 | #99 | semidirect |
| 170. C173 | #1898 | semidirect |
| 175. C2×#99 | D173 | semidirect |
| 207. C24 | C4×D173 | semidirect |
| 225. C22×C4 | C4×D173 | semidirect |
| 239. C22⋊C4 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149647 | 2 |
| C2×C22⋊C4×D173 | 2 |
| C2×#19149594 | 2 |
| #26011346 | 2 |
| #26011257 | 2 |
| C2×#99×C173 | 2 |
| #1898 | 173 |