Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
590 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 151 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. D7×#499 | C2 | semidirect |
| 3. C7×#2245 | C2 | semidirect |
| 4. #11729106 | C2 | semidirect |
| 5. #11729065 | C2 | semidirect |
| 6. #11726975 | C2 | semidirect |
| 7. #11726970 | C2 | semidirect |
| 8. #11726834 | C2 | semidirect |
| 9. #11726825 | C2 | semidirect |
| 75. #2245 | D7 | semidirect |
| 279. C7 | #33708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D7×#499 | 2 |
| #11739244 | 2 |
| C7×#2245 | 2 |
| #11729106 | 2 |
| #11729065 | 2 |
| #11726975 | 2 |
| #11726970 | 2 |
| #11726834 | 2 |
| #11726825 | 2 |
| #33708 | 7 |