Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
3250 conjugacy classes of subgroups.
The subgroup lattice has 246 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11739956 | C2 | semidirect |
| 4. C4×#6511 | C2 | semidirect |
| 5. #11739647 | C2 | semidirect |
| 6. C2×C4×#1136 | C2 | semidirect |
| 15. #90510 | C4 | direct (N × H) |
| 18. #89769 | C22 | semidirect |
| 21. C4×#1136 | C22 | semidirect |
| 22. C4×#1136 | C22 | semidirect |
| 23. C2×#6377 | C22 | semidirect |
| 24. C2×C4×C7⋊C8 | C22 | semidirect |
| 47. #6511 | C2×C4 | semidirect |
| 48. C2×#1136 | C2×C4 | semidirect |
| 89. #1136 | C22×C4 | semidirect |
| 90. C2×C7⋊C8 | C22×C4 | semidirect |
| 171. C4×C7 | #568 | semidirect |
| 228. C7 | C4×#568 | semidirect |
| 239. C4 | #90510 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×#41 | 2 |
| C2×#90510 | 2 |
| #11739956 | 2 |
| C4×#6511 | 2 |
| #11739647 | 2 |
| C2×C4×#1136 | 2 |
| C4×#568 | 7 |