Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
10894 conjugacy classes of subgroups; only the 3815 normal subgroups are shown.
This group has 10894 conjugacy classes of subgroups — too many to draw. Only its 3815 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C24×D28 |
| commutator, cosocle | C4×C7 | C26 |
| Frattini | C4 | C25×D7 |
| Fitting | C7×#3573 | C2 |
| socle | C2×C7 | C24×D4 |
| hypercenter | #3573 | D7 |
| hypocenter | C7 | #63091 |
| LCS | G ▷ C4×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C2 ◁ #585 ◁ #3573 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11744566 | C2 | semidirect |
| 2. C7×#3573 | C2 | semidirect |
| 3. #11744235 | C2 | semidirect |
| 4. #11744231 | C2 | semidirect |
| 5. C2×#90443 | C2 | semidirect |
| 9. #90616 | C22 | semidirect |
| 10. C2×#6553 | C22 | semidirect |
| 11. C7×#568 | C22 | semidirect |
| 12. C2×C7×#131 | C22 | semidirect |
| 13. #90444 | C22 | semidirect |
| 14. #90443 | C22 | semidirect |
| 15. #90443 | C22 | semidirect |
| 16. #90442 | C22 | semidirect |
| 17. #90439 | C22 | semidirect |
| 18. C2×#6471 | C22 | semidirect |
| 19. C2×#6467 | C22 | semidirect |
| 20. C22×D56 | C22 | semidirect |
| 25. #6554 | C23 | semidirect |
| 27. #6553 | C23 | semidirect |
| 33. C2×#1157 | C23 | semidirect |
| 34. C22×D28 | C23 | semidirect |
| 35. C7×#131 | C23 | semidirect |
| 36. C7×#131 | C23 | semidirect |
| 37. C2×C7×M16 | C23 | semidirect |
| 38. C22×C7×C8 | C23 | semidirect |
| 39. #6472 | C23 | semidirect |
| 40. #6471 | C23 | semidirect |
| 41. C2×Dic28 | C23 | semidirect |
| 42. #6467 | C23 | semidirect |
| 43. #6467 | C23 | semidirect |
| 44. C2×D56 | C23 | semidirect |
| 45. C2×D56 | C23 | semidirect |
| 46. C2×#1132 | C23 | semidirect |
| 51. #3573 | D7 | semidirect |
| 90. #568 | C2×D7 | semidirect |
| 91. C2×#131 | C2×D7 | semidirect |
| 129. #131 | C22×D7 | semidirect |
| 130. #131 | C22×D7 | semidirect |
| 131. C2×M16 | C22×D7 | semidirect |
| 132. C22×C8 | C22×D7 | semidirect |
| 184. C7 | #63091 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11744566 | 2 |
| C7×#3573 | 2 |
| #11744235 | 2 |
| #11744231 | 2 |
| C2×#90443 | 2 |
| #63091 | 7 |