Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
3550 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 3550 conjugacy classes of subgroups — too many to draw. Only its 667 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 |
|---|---|---|
| 3. C2×#89719 | C2 | semidirect |
| 4. #11731289 | C2 | direct (N × H) |
| 6. C23×Dic14 | C22 | semidirect |
| 11. C2×C7⋊#95 | C22 | semidirect |
| 12. #89719 | C22 | semidirect |
| 15. C25×C7 | Q8 | semidirect |
| 21. C22×Dic14 | C23 | semidirect |
| 26. C7⋊#95 | C23 | semidirect |
| 37. C24×C7 | C2×Q8 | semidirect |
| 74. C25 | Dic14 | semidirect |
| 103. C24 | C2×Dic14 | semidirect |
| 115. C2×C7 | #2840 | semidirect |
| 135. C7 | C2×#2840 | semidirect |
| 148. C2 | #11731289 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#379 | 2 |
| C2×#90019 | 2 |
| C2×#89719 | 2 |
| #11731289 | 2 |
| C2×#2840 | 7 |