Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
174 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 1. C2×#19149624 | C2 | semidirect |
| 2. C2×#19149623 | C2 | semidirect |
| 4. #26011585 | C2 | semidirect |
| 5. #26011309 | C2 | semidirect |
| 6. #26011291 | C2 | semidirect |
| 7. #357×C173 | C2 | semidirect |
| 26. Dic692 | D4 | semidirect |
| 71. Dic173 | SD32 | semidirect |
| 77. C173 | #2207 | semidirect |
| 85. #357 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149624 | 2 |
| C2×#19149623 | 2 |
| #26011866 | 2 |
| #26011585 | 2 |
| #26011309 | 2 |
| #26011291 | 2 |
| #357×C173 | 2 |
| #2207 | 173 |