Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
3464 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 365 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×C22⋊C4×D173 | C2 | semidirect |
| 3. #26011347 | C2 | semidirect |
| 4. #26011346 | C2 | semidirect |
| 5. #379×C173 | C2 | semidirect |
| 7. C24×D173 | C4 | semidirect |
| 10. C22×C4×D173 | C22 | semidirect |
| 11. C2×C22⋊Dic173 | C22 | semidirect |
| 12. C2×#14583803 | C22 | semidirect |
| 15. C2×C22⋊C4×C173 | C22 | semidirect |
| 22. C23×D173 | C2×C4 | semidirect |
| 26. C22×Dic173 | C23 | semidirect |
| 31. C24×C173 | C2×C4 | semidirect |
| 33. C22×C4×C173 | C23 | semidirect |
| 42. C22×D173 | C22⋊C4 | semidirect |
| 59. C22×C173 | C2×C22⋊C4 | semidirect |
| 67. C2×D173 | C2×C22⋊C4 | semidirect |
| 75. D173 | #379 | direct (N × H) |
| 76. C173 | C2×#379 | semidirect |
| 82. #379 | D173 | direct (N × H) |
| 92. C2×C22⋊C4 | C2×D173 | semidirect |
| 104. C24 | C4×D173 | semidirect |
| 108. C22×C4 | C22×D173 | semidirect |
| 143. C22 | C22⋊C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×D173 | 2 |
| C2×C22⋊C4×D173 | 2 |
| #26011347 | 2 |
| #26011346 | 2 |
| #379×C173 | 2 |
| C2×#379 | 173 |