Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
408 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 85 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×#19149594 | C2 | semidirect |
| 3. C2×#19149593 | C2 | semidirect |
| 4. C2×#19149593 | C2 | semidirect |
| 5. #26011349 | C2 | semidirect |
| 6. C22⋊C4×Dic173 | C2 | semidirect |
| 7. C2×#99×C173 | C2 | semidirect |
| 8. C22×C22⋊D173 | C4 | semidirect |
| 16. C2×#14583805 | C4 | semidirect |
| 17. C2×C22⋊Dic173 | C4 | semidirect |
| 20. C2×#14583803 | C4 | semidirect |
| 59. C22⋊Dic173 | D4 | semidirect |
| 77. C22⋊C4×C173 | D4 | semidirect |
| 171. Dic173 | #99 | semidirect |
| 183. C173 | #1964 | semidirect |
| 189. C2×#99 | D173 | semidirect |
| 260. 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×#19149651 | 2 |
| C2×#19149594 | 2 |
| C2×#19149593 | 2 |
| #26011349 | 2 |
| C22⋊C4×Dic173 | 2 |
| C2×#99×C173 | 2 |
| #1964 | 173 |