Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
340 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #11725588 | C2 | direct (N × H) |
| 5. C2×C7×#125 | C4 | semidirect |
| 9. C7×#488 | C4 | semidirect |
| 13. C2×C4×C7×C8 | C4 | semidirect |
| 26. C7×#125 | C2×C4 | semidirect |
| 43. C4×C7×C8 | C2×C4 | semidirect |
| 87. C2×#125 | Dic7 | semidirect |
| 91. #488 | Dic7 | semidirect |
| 97. C2×C4×C8 | Dic7 | semidirect |
| 137. #125 | C2×Dic7 | semidirect |
| 157. C4×C8 | C2×Dic7 | semidirect |
| 215. C2×C7 | #1414 | semidirect |
| 246. C7 | C2×#1414 | semidirect |
| 269. C2 | #11725588 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#488 | 2 |
| C2×#89337 | 2 |
| C2×#89336 | 2 |
| #11725588 | 2 |
| C2×#1414 | 7 |