Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
560 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 161 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×#19149638 | C2 | semidirect |
| 3. #26011431 | C2 | semidirect |
| 4. #26011428 | C2 | semidirect |
| 5. #26011423 | C2 | semidirect |
| 6. #26011418 | C2 | semidirect |
| 7. #26011416 | C2 | semidirect |
| 9. C4×C4⋊Dic173 | C2 | semidirect |
| 10. C4×#14583803 | C2 | semidirect |
| 11. C4×C22⋊C4×C173 | C2 | semidirect |
| 137. C173 | #2395 | semidirect |
| 149. C4×C22⋊C4 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D173 | 2 |
| C2×#19149638 | 2 |
| #26011431 | 2 |
| #26011428 | 2 |
| #26011423 | 2 |
| #26011418 | 2 |
| #26011416 | 2 |
| #26011407 | 2 |
| C4×C4⋊Dic173 | 2 |
| C4×#14583803 | 2 |
| C4×C22⋊C4×C173 | 2 |
| #2395 | 173 |