Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
3464 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 549 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 |
|---|---|---|
| 1. C22×C22⋊Dic173 | C2 | semidirect |
| 2. #26011347 | C2 | direct (N × H) |
| 4. C23×Dic173 | C22 | semidirect |
| 6. C2×C22⋊Dic173 | C22 | semidirect |
| 8. C25×C173 | C4 | semidirect |
| 12. C22×Dic173 | C23 | semidirect |
| 19. C24×C173 | C2×C4 | semidirect |
| 31. C23×C173 | C22⋊C4 | semidirect |
| 42. C22×C173 | C2×C22⋊C4 | semidirect |
| 48. C2×C173 | #379 | semidirect |
| 51. C173 | C2×#379 | semidirect |
| 57. C25 | Dic173 | semidirect |
| 68. C24 | C2×Dic173 | semidirect |
| 81. C23 | C22⋊Dic173 | semidirect |
| 94. C22 | C2×C22⋊Dic173 | semidirect |
| 100. C2 | #26011347 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic173 | 2 |
| #26011347 | 2 |
| C26×C173 | 2 |
| C2×#379 | 173 |