Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
278 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 3. #11728411 | C2 | semidirect |
| 5. C7×#1384 | C2 | semidirect |
| 6. #11725621 | C2 | semidirect |
| 7. #11725530 | C2 | semidirect |
| 58. #1384 | D7 | semidirect |
| 253. C7 | #13489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11729196 | 2 |
| #11728412 | 2 |
| #11728411 | 2 |
| #11728405 | 2 |
| C7×#1384 | 2 |
| #11725621 | 2 |
| #11725530 | 2 |
| #13489 | 7 |