Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
484 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 189 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. #26011372 | C2 | semidirect |
| 4. #26011357 | C2 | semidirect |
| 6. C4⋊C4×Dic173 | C2 | semidirect |
| 7. #384×C173 | C2 | semidirect |
| 9. #19149636 | C4 | semidirect |
| 88. C173 | #2314 | semidirect |
| 93. #384 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149636 | 2 |
| #26011381 | 2 |
| #26011372 | 2 |
| #26011357 | 2 |
| #26011348 | 2 |
| C4⋊C4×Dic173 | 2 |
| #384×C173 | 2 |
| #2314 | 173 |