Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
290 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. C7×#1363 | C2 | semidirect |
| 5. #11725605 | C2 | semidirect |
| 6. #11725369 | C2 | semidirect |
| 7. #11725274 | C2 | semidirect |
| 67. #1363 | D7 | semidirect |
| 255. C7 | #11967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D7×#499 | 2 |
| #11727028 | 2 |
| #11726284 | 2 |
| C7×#1363 | 2 |
| #11725605 | 2 |
| #11725369 | 2 |
| #11725274 | 2 |
| #11967 | 7 |