Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
542 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 101 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. #11740785 | C2 | semidirect |
| 4. #11729592 | C2 | semidirect |
| 6. #11728547 | C2 | semidirect |
| 7. #11725547 | C2 | semidirect |
| 130. C2×C7⋊C8 | SD16 | semidirect |
| 345. C7 | #10220 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3208 | 2 |
| #11740785 | 2 |
| #11740614 | 2 |
| #11729592 | 2 |
| #11729519 | 2 |
| #11728547 | 2 |
| #11725547 | 2 |
| #10220 | 7 |