Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
380 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. #26011349 | C2 | semidirect |
| 4. #26011257 | C2 | semidirect |
| 6. C23×Dic173 | C4 | semidirect |
| 10. C2×C4⋊Dic173 | C4 | semidirect |
| 12. C2×C22⋊Dic173 | C4 | semidirect |
| 15. C2×C4×Dic173 | C4 | semidirect |
| 72. C23×C173 | C4⋊C4 | semidirect |
| 85. C2×C4×C173 | C4⋊C4 | semidirect |
| 110. Dic173 | #99 | semidirect |
| 119. C173 | #1799 | semidirect |
| 176. C23 | #14583805 | semidirect |
| 205. C2×C4 | #14583805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic173 | 2 |
| C2×#19149594 | 2 |
| #26011349 | 2 |
| #26011257 | 2 |
| C2×#99×C173 | 2 |
| #1799 | 173 |