Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
390 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 3. #11725590 | C2 | direct (N × H) |
| 5. C2×C7×#125 | C4 | semidirect |
| 7. C7×#490 | C4 | semidirect |
| 10. C2×C7×#97 | C4 | semidirect |
| 24. C7×#125 | C2×C4 | semidirect |
| 32. C7×#97 | C2×C4 | semidirect |
| 65. C2×#125 | Dic7 | semidirect |
| 67. #490 | Dic7 | semidirect |
| 71. C2×#97 | Dic7 | semidirect |
| 107. #125 | C2×Dic7 | semidirect |
| 117. #97 | C2×Dic7 | semidirect |
| 164. C2×C7 | #1412 | semidirect |
| 190. C7 | C2×#1412 | semidirect |
| 211. C2 | #11725590 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#490 | 2 |
| C2×#89340 | 2 |
| #11725590 | 2 |
| C2×#1412 | 7 |