Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2186 conjugacy classes of subgroups; only the 591 normal subgroups are shown.
This group has 2186 conjugacy classes of subgroups — too many to draw. Only its 591 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D7 |
| commutator, socle, cosocle | C23×C7 | C25 |
| Fitting | C7×#2866 | C2 |
| prime radical | C24×D7 | C23 |
| hypercenter | #2866 | D7 |
| hypocenter | C7 | C2×#2866 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #2866 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#2866 | C2 | semidirect |
| 3. #11733268 | C2 | semidirect |
| 4. D7×#387 | C2 | semidirect |
| 5. #11732739 | C2 | semidirect |
| 6. #11730762 | C2 | semidirect |
| 7. C43×D7 | C2 | semidirect |
| 12. C7×#387 | C22 | semidirect |
| 13. C43×C7 | C22 | semidirect |
| 15. #89753 | C22 | semidirect |
| 16. #89750 | C22 | semidirect |
| 21. #89705 | C22 | semidirect |
| 22. C42×Dic7 | C22 | semidirect |
| 27. #89427 | C22 | semidirect |
| 28. #89426 | C22 | semidirect |
| 29. #89425 | C22 | semidirect |
| 30. #89424 | C22 | semidirect |
| 61. #2866 | D7 | direct (N × H) |
| 109. #387 | C2×D7 | semidirect |
| 113. C43 | C2×D7 | semidirect |
| 197. D7 | #2866 | direct (N × H) |
| 217. C7 | C2×#2866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2866 | 2 |
| D7×#388 | 2 |
| #11733268 | 2 |
| D7×#387 | 2 |
| #11732739 | 2 |
| #11730762 | 2 |
| C43×D7 | 2 |
| C2×#2866 | 7 |