Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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. #26011827 | C2 | semidirect |
| 3. #26011732 | C2 | semidirect |
| 4. #26011649 | C2 | semidirect |
| 7. C2×Dic692 | C22 | semidirect |
| 15. #19149613 | C22 | semidirect |
| 16. #19149604 | C22 | semidirect |
| 48. C23×C173 | Q16 | semidirect |
| 77. C173 | #3189 | semidirect |
| 120. C23 | Dic692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149658 | 2 |
| #26011827 | 2 |
| #26011732 | 2 |
| #26011649 | 2 |
| C2×C22⋊C8×C173 | 2 |
| #3189 | 173 |