Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
338 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 12. C2×Dic692 | C4 | semidirect |
| 86. C2×C4×C173 | Q16 | semidirect |
| 119. C173 | #1878 | semidirect |
| 206. C2×C4 | Dic692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic692 | 2 |
| C2×C4×Dic346 | 2 |
| C2×#19149604 | 2 |
| #26011397 | 2 |
| #26011254 | 2 |
| #336×C173 | 2 |
| #1878 | 173 |