Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
426 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 97 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. #11736712 | C2 | semidirect |
| 4. #11727616 | C2 | semidirect |
| 6. C7×#1278 | C2 | semidirect |
| 7. #11725462 | C2 | semidirect |
| 81. #1278 | D7 | semidirect |
| 334. C7 | #9070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736712 | 2 |
| #11735908 | 2 |
| #11728515 | 2 |
| #11727616 | 2 |
| #11727607 | 2 |
| C7×#1278 | 2 |
| #11725462 | 2 |
| #9070 | 7 |