Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
390 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 103 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. #11740776 | C2 | semidirect |
| 3. #11729585 | C2 | semidirect |
| 6. #11725562 | C2 | semidirect |
| 7. #11725561 | C2 | semidirect |
| 296. C7 | #9372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3235 | 2 |
| #11740776 | 2 |
| #11729585 | 2 |
| #11729554 | 2 |
| #11729553 | 2 |
| #11725562 | 2 |
| #11725561 | 2 |
| #9372 | 7 |