Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
228 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #26011529 | C2 | semidirect |
| 3. #26011296 | C2 | semidirect |
| 4. #26011293 | C2 | semidirect |
| 5. C22×C16×C173 | C2 | semidirect |
| 8. #19149701 | C4 | semidirect |
| 69. C173 | #2138 | semidirect |
| 72. C22×C16 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149701 | 2 |
| #26011529 | 2 |
| #26011296 | 2 |
| #26011293 | 2 |
| C22×C16×C173 | 2 |
| #2138 | 173 |