Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
708 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 708 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 |
|---|---|---|
| 2. C2×#19149710 | C2 | semidirect |
| 3. #26011673 | C2 | direct (N × H) |
| 4. C2×#19149607 | C2 | semidirect |
| 5. C2×#19149598 | C2 | semidirect |
| 6. C2×C4⋊Q8×C173 | C2 | semidirect |
| 15. #19149710 | C22 | semidirect |
| 19. #19149607 | C22 | semidirect |
| 20. #19149598 | C22 | semidirect |
| 24. C4⋊Q8×C173 | C22 | semidirect |
| 109. C2×C173 | #456 | semidirect |
| 112. C173 | C2×#456 | semidirect |
| 116. C2×C4⋊Q8 | D173 | semidirect |
| 135. C4⋊Q8 | C2×D173 | semidirect |
| 223. C2 | #26011673 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149727 | 2 |
| C2×#19149710 | 2 |
| #26011673 | 2 |
| C2×#19149607 | 2 |
| C2×#19149598 | 2 |
| C2×C4⋊Q8×C173 | 2 |
| C2×#456 | 173 |