Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
316 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 161 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 |
|---|---|---|
| 11. #19149608 | C4 | semidirect |
| 22. C4×Dic173 | C8 | semidirect |
| 58. Dic173 | C4×C8 | semidirect |
| 59. Dic173 | C4⋊C8 | semidirect |
| 65. C173 | C4×C4⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149608 | 2 |
| C2×C8×Dic173 | 2 |
| C42×Dic173 | 2 |
| #26011246 | 2 |
| #336×C173 | 2 |
| C4×C4⋊C8 | 173 |