Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
456 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 121 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. C22×C4⋊Dic173 | C2 | semidirect |
| 3. C2×#19149601 | C2 | semidirect |
| 4. #26011254 | C2 | semidirect |
| 5. C2×C22⋊C8×C173 | C2 | semidirect |
| 10. #19149653 | C4 | semidirect |
| 24. C2×D692 | C2×C4 | semidirect |
| 36. C4⋊Dic173 | C2×C4 | semidirect |
| 37. C4⋊Dic173 | D4 | semidirect |
| 90. C22×C173 | #102 | semidirect |
| 119. C173 | #1874 | semidirect |
| 124. C2×C22⋊C8 | D173 | semidirect |
| 217. C22 | #19149601 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149653 | 2 |
| C22×C4⋊Dic173 | 2 |
| C2×#19149601 | 2 |
| #26011254 | 2 |
| C2×C22⋊C8×C173 | 2 |
| #1874 | 173 |