Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
278 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 1. #26012117 | C2 | semidirect |
| 4. #26011258 | C2 | semidirect |
| 5. #26011257 | C2 | semidirect |
| 6. #26011257 | C2 | semidirect |
| 36. C24×C173 | Q8 | semidirect |
| 46. C22×C4×C173 | Q8 | semidirect |
| 117. C173 | #2032 | semidirect |
| 139. C24 | Dic346 | semidirect |
| 154. C22×C4 | Dic346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012117 | 2 |
| C2×#19149594 | 2 |
| #26011258 | 2 |
| #26011257 | 2 |
| C2×#99×C173 | 2 |
| #2032 | 173 |