Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
466 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11729834 | C2 | semidirect |
| 3. #11729830 | C2 | semidirect |
| 4. C2×#89358 | C2 | semidirect |
| 5. #11729787 | C2 | semidirect |
| 6. #11727650 | C2 | semidirect |
| 7. #11727638 | C2 | semidirect |
| 13. C7×#495 | C4 | semidirect |
| 14. C7×#493 | C4 | semidirect |
| 65. #6386 | D4 | semidirect |
| 67. C2×C7⋊C16 | D4 | semidirect |
| 132. #495 | Dic7 | semidirect |
| 133. #493 | Dic7 | semidirect |
| 325. C7 | #13215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3155 | 2 |
| #11729834 | 2 |
| #11729830 | 2 |
| C2×#89358 | 2 |
| #11729787 | 2 |
| #11727650 | 2 |
| #11727638 | 2 |
| #13215 | 7 |