Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
368 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 85 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×#19149612 | C2 | semidirect |
| 3. C2×#19149601 | C2 | semidirect |
| 4. C2×#19149599 | C2 | semidirect |
| 5. C2×#19149591 | C2 | semidirect |
| 6. #26011348 | C2 | semidirect |
| 7. #340×C173 | C2 | semidirect |
| 46. C2×#13063436 | D4 | semidirect |
| 143. C173 | #2033 | semidirect |
| 151. #340 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149654 | 2 |
| C2×#19149612 | 2 |
| C2×#19149601 | 2 |
| C2×#19149599 | 2 |
| C2×#19149591 | 2 |
| #26011348 | 2 |
| #340×C173 | 2 |
| #2033 | 173 |