Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
668 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 151 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. #11739458 | C2 | semidirect |
| 2. #11737339 | C2 | semidirect |
| 3. C7×#2170 | C2 | semidirect |
| 4. #11729208 | C2 | semidirect |
| 5. #11727059 | C2 | semidirect |
| 6. #11726880 | C2 | semidirect |
| 7. #11726821 | C2 | semidirect |
| 8. #11726814 | C2 | semidirect |
| 10. #90443 | C22 | semidirect |
| 11. C7×#504 | C22 | semidirect |
| 13. #89914 | C22 | semidirect |
| 15. #89680 | C22 | semidirect |
| 19. C2×D112 | C22 | semidirect |
| 20. C2×D112 | C22 | semidirect |
| 23. #89472 | C22 | semidirect |
| 24. #89467 | C22 | semidirect |
| 25. C7×#364 | C22 | semidirect |
| 26. C7×#350 | C22 | semidirect |
| 27. C4×C7×C16 | C22 | semidirect |
| 28. #89311 | C22 | semidirect |
| 29. #89305 | C22 | semidirect |
| 30. #89301 | C22 | semidirect |
| 59. Dic56 | D4 | semidirect |
| 61. #6374 | D4 | semidirect |
| 66. D112 | D4 | semidirect |
| 74. #2170 | D7 | semidirect |
| 120. #504 | C2×D7 | semidirect |
| 128. #364 | C2×D7 | semidirect |
| 131. #350 | C2×D7 | semidirect |
| 132. C4×C16 | C2×D7 | semidirect |
| 268. C7 | #33858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739458 | 2 |
| #11737339 | 2 |
| C7×#2170 | 2 |
| #11729208 | 2 |
| #11727059 | 2 |
| #11726880 | 2 |
| #11726821 | 2 |
| #11726814 | 2 |
| #33858 | 7 |