Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
554 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. #11741352 | C2 | semidirect |
| 3. C22×#6374 | C2 | semidirect |
| 4. C2×C7×#359 | C2 | semidirect |
| 5. #11728463 | C2 | semidirect |
| 6. C2×#89291 | C2 | semidirect |
| 7. #11725611 | C2 | semidirect |
| 85. C2×#359 | D7 | semidirect |
| 377. C7 | #13337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741352 | 2 |
| C2×#89965 | 2 |
| C22×#6374 | 2 |
| C2×C7×#359 | 2 |
| #11728463 | 2 |
| C2×#89291 | 2 |
| #11725611 | 2 |
| #13337 | 7 |