Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
656 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 245 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. #26011360 | C2 | semidirect |
| 4. #26011357 | C2 | semidirect |
| 6. #26011342 | C2 | semidirect |
| 7. #382×C173 | C2 | semidirect |
| 17. C42×D173 | C4 | semidirect |
| 54. C4×D173 | C4⋊C4 | semidirect |
| 76. Dic173 | #117 | semidirect |
| 82. C173 | #2285 | semidirect |
| 88. #382 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149637 | 2 |
| C2×C42×D173 | 2 |
| #26011360 | 2 |
| #26011357 | 2 |
| #26011350 | 2 |
| #26011342 | 2 |
| #382×C173 | 2 |
| #2285 | 173 |