Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
338 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 67 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. #11729042 | C2 | semidirect |
| 3. #11727044 | C2 | semidirect |
| 4. #11726343 | C2 | semidirect |
| 5. C7×#1361 | C2 | semidirect |
| 6. #11725364 | C2 | semidirect |
| 7. #11725277 | C2 | semidirect |
| 57. #1361 | D7 | semidirect |
| 249. C7 | #12384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739223 | 2 |
| #11729042 | 2 |
| #11727044 | 2 |
| #11726343 | 2 |
| C7×#1361 | 2 |
| #11725364 | 2 |
| #11725277 | 2 |
| #12384 | 7 |