Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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. #26011539 | C2 | semidirect |
| 5. #26011263 | C2 | semidirect |
| 6. #26011251 | C2 | semidirect |
| 7. C4×M16×C173 | C2 | semidirect |
| 16. #19149597 | C4 | semidirect |
| 17. #19149595 | C4 | semidirect |
| 95. C173 | #1932 | semidirect |
| 101. C4×M16 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011539 | 2 |
| #26011507 | 2 |
| C2×#19149607 | 2 |
| #26011473 | 2 |
| #26011263 | 2 |
| #26011251 | 2 |
| C4×M16×C173 | 2 |
| #1932 | 173 |