Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
696 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 177 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. C2×#19149668 | C2 | semidirect |
| 3. C22×C4×Dic173 | C2 | semidirect |
| 4. #26011398 | C2 | semidirect |
| 5. #26011392 | C2 | semidirect |
| 6. #26011381 | C2 | semidirect |
| 7. #26011368 | C2 | semidirect |
| 8. #26011356 | C2 | semidirect |
| 9. C2×C22⋊Q8×C173 | C2 | semidirect |
| 49. C4×Dic173 | D4 | semidirect |
| 103. C22×C173 | #124 | semidirect |
| 128. C173 | #2850 | semidirect |
| 131. C2×C22⋊Q8 | D173 | semidirect |
| 237. C22 | #19149668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149668 | 2 |
| C2×#19149653 | 2 |
| C22×C4×Dic173 | 2 |
| #26011398 | 2 |
| #26011392 | 2 |
| #26011381 | 2 |
| #26011368 | 2 |
| #26011356 | 2 |
| C2×C22⋊Q8×C173 | 2 |
| #2850 | 173 |