Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
312 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 312 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 |
|---|---|---|
| 3. C2×#19149742 | C2 | semidirect |
| 4. D173⋊#101 | C2 | semidirect |
| 5. #26012370 | C2 | semidirect |
| 6. #26012366 | C2 | semidirect |
| 24. #19149712 | C4 | semidirect |
| 26. #19149710 | C4 | semidirect |
| 27. #19149709 | C4 | semidirect |
| 32. #137×C173 | C4 | semidirect |
| 147. C173 | #1908 | semidirect |
| 163. #137 | #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×#19149742 | 2 |
| D173⋊#101 | 2 |
| #26012370 | 2 |
| #26012366 | 2 |
| #137×D173 | 2 |
| #1908 | 173 |