Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
306 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 99 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. C7×#1564 | C2 | semidirect |
| 3. #11727498 | C2 | semidirect |
| 4. #11725274 | C2 | semidirect |
| 5. #11725273 | C2 | semidirect |
| 57. #1564 | D7 | semidirect |
| 250. C7 | #11943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11735914 | 2 |
| C7×#1564 | 2 |
| #11727498 | 2 |
| #11725274 | 2 |
| #11725273 | 2 |
| #11943 | 7 |