Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
334 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #26011499 | C2 | semidirect |
| 5. #26011397 | C2 | semidirect |
| 6. #26011259 | C2 | semidirect |
| 7. #339×C173 | C2 | semidirect |
| 11. #19149712 | C4 | semidirect |
| 37. C2×Dic346 | C2×C4 | semidirect |
| 58. M16×C173 | C2×C4 | semidirect |
| 124. C173 | #1882 | semidirect |
| 132. #339 | D173 | semidirect |
| 177. M16 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149712 | 2 |
| #26011971 | 2 |
| C2×#19149607 | 2 |
| #26011499 | 2 |
| #26011397 | 2 |
| #26011259 | 2 |
| #339×C173 | 2 |
| #1882 | 173 |