Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 216 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 |
|---|---|---|
| 2. #26011934 | C2 | semidirect |
| 3. C2×#19149624 | C2 | semidirect |
| 4. #26011766 | C2 | semidirect |
| 5. #26011305 | C2 | semidirect |
| 6. #26011299 | C2 | semidirect |
| 7. #350×C173 | C2 | semidirect |
| 14. C2×Dic692 | C22 | semidirect |
| 20. #19149615 | C22 | semidirect |
| 23. M32×C173 | C22 | semidirect |
| 24. C2×C16×C173 | C22 | semidirect |
| 91. C173 | #2194 | semidirect |
| 99. #350 | D173 | semidirect |
| 113. M32 | C2×D173 | semidirect |
| 114. C2×C16 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012296 | 2 |
| #26011934 | 2 |
| C2×#19149624 | 2 |
| #26011766 | 2 |
| #26011305 | 2 |
| #26011299 | 2 |
| #350×C173 | 2 |
| #2194 | 173 |