Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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×#19149612 | C2 | semidirect |
| 4. #26011253 | C2 | semidirect |
| 12. C22⋊#13063436 | C4 | semidirect |
| 24. C2×#13063436 | C2×C4 | semidirect |
| 74. C22×C173 | #107 | semidirect |
| 96. C173 | #1852 | semidirect |
| 171. C22 | #19149612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic173 | 2 |
| C2×#19149612 | 2 |
| C2×C22⋊#13063436 | 2 |
| #26011253 | 2 |
| #380×C173 | 2 |
| #1852 | 173 |