Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
10698 conjugacy classes of subgroups; only the 3815 normal subgroups are shown.
This group has 10698 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 | #63093 |
| 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. #11744564 | C2 | semidirect |
| 2. C7×#3573 | C2 | semidirect |
| 3. #11744236 | C2 | semidirect |
| 4. C2×#90444 | C2 | semidirect |
| 5. #11744231 | C2 | semidirect |
| 9. #90616 | C22 | semidirect |
| 10. C2×#6554 | C22 | semidirect |
| 11. C7×#568 | C22 | semidirect |
| 12. C2×C7×#131 | C22 | semidirect |
| 13. #90444 | C22 | semidirect |
| 14. #90444 | C22 | semidirect |
| 15. #90443 | C22 | semidirect |
| 16. #90442 | C22 | semidirect |
| 17. #90439 | C22 | semidirect |
| 18. C2×#6472 | C22 | semidirect |
| 19. C22×Dic28 | C22 | semidirect |
| 20. C2×#6467 | C22 | semidirect |
| 51. #3573 | D7 | semidirect |
| 90. #568 | C2×D7 | semidirect |
| 91. C2×#131 | C2×D7 | semidirect |
| 182. C7 | #63093 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11744564 | 2 |
| C7×#3573 | 2 |
| #11744236 | 2 |
| C2×#90444 | 2 |
| #11744231 | 2 |
| #63093 | 7 |