Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
354 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 4. #11729182 | C2 | semidirect |
| 5. C2×#89306 | C2 | semidirect |
| 6. #11728458 | C2 | semidirect |
| 7. #11725538 | C2 | semidirect |
| 268. C7 | #13478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#361 | 2 |
| #11729792 | 2 |
| #11729787 | 2 |
| #11729182 | 2 |
| C2×#89306 | 2 |
| #11728458 | 2 |
| #11725538 | 2 |
| #13478 | 7 |