Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
388 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 3. #11725590 | C2 | semidirect |
| 4. C7×#533 | C4 | semidirect |
| 6. C7×#490 | C4 | semidirect |
| 10. C4×C7×M16 | C4 | semidirect |
| 23. C7×#125 | C2×C4 | semidirect |
| 31. C7×#97 | C2×C4 | semidirect |
| 64. #533 | Dic7 | semidirect |
| 66. #490 | Dic7 | semidirect |
| 71. C4×M16 | Dic7 | semidirect |
| 105. #125 | C2×Dic7 | semidirect |
| 115. #97 | C2×Dic7 | semidirect |
| 186. C7 | #13595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3138 | 2 |
| C2×#89340 | 2 |
| #11725590 | 2 |
| #13595 | 7 |