Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
472 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 91 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. #11736774 | C2 | semidirect |
| 3. #11728582 | C2 | semidirect |
| 4. #11728558 | C2 | semidirect |
| 5. #11728552 | C2 | semidirect |
| 6. C7×#1307 | C2 | semidirect |
| 7. #11725516 | C2 | semidirect |
| 89. #1307 | D7 | semidirect |
| 386. C7 | #9350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736774 | 2 |
| #11736503 | 2 |
| #11728582 | 2 |
| #11728558 | 2 |
| #11728552 | 2 |
| C7×#1307 | 2 |
| #11725516 | 2 |
| #9350 | 7 |