Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
474 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. C2×#89340 | C2 | semidirect |
| 3. #11725598 | C2 | semidirect |
| 4. #11725594 | C2 | semidirect |
| 6. C7×#532 | C4 | semidirect |
| 9. C7×#493 | C4 | semidirect |
| 11. C7×#492 | C4 | semidirect |
| 13. C4×C7×M16 | C4 | semidirect |
| 28. C7×C4⋊Q8 | C2×C4 | semidirect |
| 31. C7×#127 | C2×C4 | semidirect |
| 40. C4×C7×C8 | C2×C4 | semidirect |
| 41. C4×C7×C8 | C2×C4 | semidirect |
| 83. #532 | Dic7 | semidirect |
| 86. #493 | Dic7 | semidirect |
| 88. #492 | Dic7 | semidirect |
| 91. C4×M16 | Dic7 | semidirect |
| 134. C4⋊Q8 | C2×Dic7 | semidirect |
| 137. #127 | C2×Dic7 | semidirect |
| 148. C4×C8 | C2×Dic7 | semidirect |
| 149. C4×C8 | C2×Dic7 | semidirect |
| 237. C7 | #13584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3151 | 2 |
| C2×#89340 | 2 |
| #11725598 | 2 |
| #11725594 | 2 |
| #13584 | 7 |