Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
600 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 229 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. #26011386 | C2 | semidirect |
| 6. #26011360 | C2 | semidirect |
| 7. #26011357 | C2 | semidirect |
| 8. #26011356 | C2 | semidirect |
| 9. #384×C173 | C2 | semidirect |
| 13. #19149636 | C4 | semidirect |
| 44. #14583805 | C2×C4 | semidirect |
| 48. C4×Dic173 | C2×C4 | semidirect |
| 56. C42×C173 | C2×C4 | semidirect |
| 73. C4×D173 | C4⋊C4 | semidirect |
| 109. C173 | #2317 | semidirect |
| 117. #384 | D173 | semidirect |
| 166. C42 | C4×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×#19149636 | 2 |
| C2×C4⋊C4×D173 | 2 |
| #26011386 | 2 |
| #26011362 | 2 |
| #26011360 | 2 |
| #26011357 | 2 |
| #26011356 | 2 |
| #384×C173 | 2 |
| #2317 | 173 |