Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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. #26011934 | C2 | semidirect |
| 3. C2×#19149623 | C2 | semidirect |
| 4. #26011767 | C2 | semidirect |
| 5. #26011297 | C2 | semidirect |
| 6. #26011276 | C2 | semidirect |
| 7. #361×C173 | C2 | semidirect |
| 14. C2×Dic692 | C22 | semidirect |
| 20. C2×#14583801 | C22 | semidirect |
| 23. M32×C173 | C22 | semidirect |
| 24. #108×C173 | C22 | semidirect |
| 91. C173 | #2194 | semidirect |
| 97. #361 | D173 | semidirect |
| 113. M32 | C2×D173 | semidirect |
| 115. #108 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012292 | 2 |
| #26011934 | 2 |
| C2×#19149623 | 2 |
| #26011767 | 2 |
| #26011297 | 2 |
| #26011276 | 2 |
| #361×C173 | 2 |
| #2194 | 173 |