Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
332 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 68 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. D173⋊#131 | C2 | semidirect |
| 2. #26012482 | C2 | semidirect |
| 3. C2×#19149741 | C2 | semidirect |
| 4. D173⋊#100 | C2 | semidirect |
| 5. #26012370 | C2 | semidirect |
| 6. #26012366 | C2 | semidirect |
| 24. #19149707 | C4 | semidirect |
| 26. #19149705 | C4 | semidirect |
| 27. #19149704 | C4 | semidirect |
| 32. AGL(1,ℤ/8)×C173 | C4 | semidirect |
| 156. C173 | #1907 | semidirect |
| 172. AGL(1,ℤ/8) | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊#131 | 2 |
| #26012482 | 2 |
| C2×#19149741 | 2 |
| D173⋊#100 | 2 |
| #26012370 | 2 |
| #26012366 | 2 |
| AGL(1,ℤ/8)×D173 | 2 |
| #1907 | 173 |