Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
680 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 145 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. #26011258 | C2 | semidirect |
| 4. #26011257 | C2 | semidirect |
| 5. #342×C173 | C2 | semidirect |
| 8. C22×C4×D173 | C4 | semidirect |
| 12. C2×#14583803 | C4 | semidirect |
| 16. C22⋊C4×D173 | C4 | semidirect |
| 28. C22×Dic173 | C2×C4 | semidirect |
| 36. C22⋊Dic173 | C2×C4 | semidirect |
| 41. C22×C4×C173 | C2×C4 | semidirect |
| 44. C22⋊C4×C173 | C2×C4 | semidirect |
| 116. D173 | #342 | direct (N × H) |
| 117. C173 | C2×#342 | semidirect |
| 123. #342 | D173 | direct (N × H) |
| 154. C22×C4 | C4×D173 | semidirect |
| 162. C22⋊C4 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊C4×D173 | 2 |
| #26011258 | 2 |
| #26011257 | 2 |
| #342×C173 | 2 |
| C2×#342 | 173 |