Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
408 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 97 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×#1548 | C2 | semidirect |
| 3. #11729529 | C2 | semidirect |
| 5. #11728504 | C2 | semidirect |
| 7. #11725520 | C2 | semidirect |
| 64. #1548 | D7 | semidirect |
| 296. C7 | #10453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89856 | 2 |
| C7×#1548 | 2 |
| #11729529 | 2 |
| #11728510 | 2 |
| #11728504 | 2 |
| #11728281 | 2 |
| #11725520 | 2 |
| #10453 | 7 |