Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
402 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 87 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×#89311 | C2 | semidirect |
| 3. #11729191 | C2 | semidirect |
| 4. #11728472 | C2 | semidirect |
| 5. C2×#89290 | C2 | semidirect |
| 6. #11728437 | C2 | semidirect |
| 7. C7×#1388 | C2 | semidirect |
| 70. #1388 | D7 | semidirect |
| 305. C7 | #13389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89669 | 2 |
| C2×#89311 | 2 |
| #11729191 | 2 |
| #11728472 | 2 |
| C2×#89290 | 2 |
| #11728437 | 2 |
| C7×#1388 | 2 |
| #13389 | 7 |