Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
354 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×#89306 | C2 | semidirect |
| 3. #11728458 | C2 | semidirect |
| 6. #11728350 | C2 | semidirect |
| 7. C7×#1387 | C2 | semidirect |
| 63. #1387 | D7 | semidirect |
| 268. C7 | #13478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11729194 | 2 |
| C2×#89306 | 2 |
| #11728458 | 2 |
| C2×#89290 | 2 |
| #11728382 | 2 |
| #11728350 | 2 |
| C7×#1387 | 2 |
| #13478 | 7 |