Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
442 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 442 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. #11736783 | C2 | semidirect |
| 3. C7×#1536 | C2 | semidirect |
| 4. #11729554 | C2 | semidirect |
| 5. #11728570 | C2 | semidirect |
| 6. #11725563 | C2 | semidirect |
| 7. #11725561 | C2 | semidirect |
| 74. #1536 | D7 | semidirect |
| 321. C7 | #9371 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740753 | 2 |
| #11736783 | 2 |
| C7×#1536 | 2 |
| #11729554 | 2 |
| #11728570 | 2 |
| #11725563 | 2 |
| #11725561 | 2 |
| #9371 | 7 |