Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
166 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 4. C2×#14583810 | C4 | semidirect |
| 5. C22×#13063436 | C4 | semidirect |
| 8. #19149594 | C4 | semidirect |
| 14. #99×C173 | C4 | semidirect |
| 74. C173 | #1391 | semidirect |
| 87. #99 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011465 | 2 |
| #26011458 | 2 |
| #410×C173 | 2 |
| #1391 | 173 |