Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
486 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 107 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. C7×#1568 | C2 | semidirect |
| 3. #11727499 | C2 | semidirect |
| 4. #11725279 | C2 | semidirect |
| 14. C7×#335 | C22 | semidirect |
| 17. C4⋊(C7⋊C16) | C22 | semidirect |
| 46. #1568 | D7 | semidirect |
| 90. #335 | C2×D7 | semidirect |
| 220. C7 | #11964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89467 | 2 |
| C7×#1568 | 2 |
| #11727499 | 2 |
| #11725279 | 2 |
| #11964 | 7 |