Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19149709 | C2 | semidirect |
| 2. C2×#19149666 | C2 | semidirect |
| 3. #41×Dic173 | C2 | semidirect |
| 4. #26011711 | C2 | semidirect |
| 5. #26011704 | C2 | semidirect |
| 6. #26011514 | C2 | semidirect |
| 7. #26011501 | C2 | semidirect |
| 8. #26011496 | C2 | semidirect |
| 12. C2×#14583816 | C22 | semidirect |
| 13. C2×#14583814 | C22 | semidirect |
| 18. Q8×Dic173 | C22 | semidirect |
| 20. D4×Dic173 | C22 | semidirect |
| 26. #19149608 | C22 | semidirect |
| 27. #19149604 | C22 | semidirect |
| 125. C173 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149709 | 2 |
| C2×#19149666 | 2 |
| #41×Dic173 | 2 |
| #26011711 | 2 |
| #26011704 | 2 |
| #26011514 | 2 |
| #26011501 | 2 |
| #26011496 | 2 |
| C2×AGL(1,ℤ/8)×C173 | 2 |
| #3040 | 173 |