Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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×#19149685 | C2 | semidirect |
| 3. C2×#19149607 | C2 | semidirect |
| 4. C2×#19149607 | C2 | semidirect |
| 5. #26011457 | C2 | semidirect |
| 6. #26011256 | C2 | semidirect |
| 7. #336×C173 | C2 | semidirect |
| 12. C2×Dic692 | C4 | semidirect |
| 13. C2×#14583815 | C4 | semidirect |
| 14. C2×#14583815 | C4 | semidirect |
| 15. C2×D1384 | C4 | semidirect |
| 130. C173 | #1876 | semidirect |
| 138. #336 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149701 | 2 |
| C2×#19149685 | 2 |
| C2×#19149607 | 2 |
| #26011457 | 2 |
| #26011256 | 2 |
| #336×C173 | 2 |
| #1876 | 173 |