Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×#19149712 | C2 | semidirect |
| 3. C2×#19149658 | C2 | semidirect |
| 4. #26011655 | C2 | semidirect |
| 5. #26011649 | C2 | semidirect |
| 6. #26011644 | C2 | semidirect |
| 7. #26011493 | C2 | semidirect |
| 8. #407×C173 | C2 | semidirect |
| 15. C22×Dic346 | C22 | semidirect |
| 20. C2×Dic692 | C22 | semidirect |
| 21. C2×#14583815 | C22 | semidirect |
| 25. #19149658 | C22 | semidirect |
| 26. C2×C4⋊Dic173 | C22 | semidirect |
| 29. #19149604 | C22 | semidirect |
| 30. #19149601 | C22 | semidirect |
| 32. C2×M16×C173 | C22 | semidirect |
| 34. C22⋊C8×C173 | C22 | semidirect |
| 126. C22×C173 | #137 | semidirect |
| 146. C173 | #3007 | semidirect |
| 155. #407 | D173 | semidirect |
| 170. C2×M16 | C2×D173 | semidirect |
| 181. C22⋊C8 | C2×D173 | semidirect |
| 277. C22 | #19149712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583826 | 2 |
| C2×#19149712 | 2 |
| C2×#19149658 | 2 |
| #26011655 | 2 |
| #26011649 | 2 |
| #26011644 | 2 |
| #26011493 | 2 |
| #407×C173 | 2 |
| #3007 | 173 |