Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#19149727 | C2 | semidirect |
| 2. C2×#19149699 | C2 | semidirect |
| 3. #26012069 | C2 | semidirect |
| 4. #26011652 | C2 | semidirect |
| 5. #26011645 | C2 | semidirect |
| 6. #26011635 | C2 | semidirect |
| 7. #26011628 | C2 | semidirect |
| 8. #26011493 | C2 | semidirect |
| 9. C2×#19149603 | C2 | semidirect |
| 10. #26011459 | C2 | semidirect |
| 11. C2×#137×C173 | C2 | semidirect |
| 52. #14583826 | D4 | semidirect |
| 86. C2×Q8×C173 | D4 | semidirect |
| 169. C173 | #3013 | semidirect |
| 172. C2×#137 | D173 | semidirect |
| 233. C2×Q8 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149727 | 2 |
| C2×#19149699 | 2 |
| #26012069 | 2 |
| #26011652 | 2 |
| #26011645 | 2 |
| #26011635 | 2 |
| #26011628 | 2 |
| #26011493 | 2 |
| C2×#19149603 | 2 |
| #26011459 | 2 |
| C2×#137×C173 | 2 |
| #3013 | 173 |