Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
400 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19149608 | C2 | semidirect |
| 4. #26011245 | C2 | semidirect |
| 24. C22×Dic173 | C8 | semidirect |
| 85. C22×C173 | C4⋊C8 | semidirect |
| 99. Dic173 | C22⋊C8 | semidirect |
| 108. C173 | #1797 | semidirect |
| 194. C22 | #19149608 | 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×#19149608 | 2 |
| C2×C22⋊#13063436 | 2 |
| #26011245 | 2 |
| C2×C22⋊C8×C173 | 2 |
| #1797 | 173 |