Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
756 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 249 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. #26012258 | C2 | semidirect |
| 3. #26011473 | C2 | semidirect |
| 4. C2×#19149595 | C2 | semidirect |
| 5. #568×C173 | C2 | semidirect |
| 13. C2×#14583810 | C22 | semidirect |
| 14. #19149597 | C22 | semidirect |
| 15. #19149595 | C22 | semidirect |
| 18. C2×M16×C173 | C22 | semidirect |
| 76. C173 | #2888 | semidirect |
| 80. #568 | D173 | semidirect |
| 93. C2×M16 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149725 | 2 |
| #26012258 | 2 |
| #26011473 | 2 |
| C2×#19149595 | 2 |
| #568×C173 | 2 |
| #2888 | 173 |