Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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. C4×Dic692 | C2 | semidirect |
| 3. #26011318 | C2 | semidirect |
| 4. #26011294 | C2 | semidirect |
| 6. C4×#14583801 | C2 | semidirect |
| 10. #19149623 | C4 | direct (N × H) |
| 22. Dic692 | C2×C4 | semidirect |
| 27. #14583801 | C2×C4 | semidirect |
| 58. C4×C173 | SD32 | semidirect |
| 67. C173 | C4×SD32 | semidirect |
| 128. C4 | #19149623 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149623 | 2 |
| C4×Dic692 | 2 |
| #26011318 | 2 |
| #26011294 | 2 |
| #26011292 | 2 |
| C4×#14583801 | 2 |
| C4×D8×C173 | 2 |
| C4×SD32 | 173 |