Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
852 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×C22⋊#13063436 | C2 | semidirect |
| 3. C22×#13063436 | C22 | semidirect |
| 12. C24×C173 | C8 | semidirect |
| 41. C22×C173 | C22⋊C8 | semidirect |
| 51. C173 | #1779 | semidirect |
| 63. C24 | #13063436 | semidirect |
| 93. C22 | C22⋊#13063436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#13063436 | 2 |
| C24×C4×C173 | 2 |
| #1779 | 173 |