Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
390 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 111 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. C4×#6391 | C2 | semidirect |
| 3. #11727499 | C2 | semidirect |
| 4. #11725580 | C2 | semidirect |
| 6. C7×#500 | C4 | semidirect |
| 7. C7×#493 | C4 | semidirect |
| 12. C4×C7×D8 | C4 | semidirect |
| 83. #500 | Dic7 | semidirect |
| 84. #493 | Dic7 | semidirect |
| 89. C4×D8 | Dic7 | semidirect |
| 229. C7 | #11744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3169 | 2 |
| C4×#6391 | 2 |
| #11727499 | 2 |
| #11725580 | 2 |
| #11744 | 7 |