Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
554 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 554 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 |
|---|---|---|
| 1. C7×#2808 | C2 | semidirect |
| 2. #11727442 | C2 | semidirect |
| 4. #11727381 | C2 | semidirect |
| 5. #11725448 | C2 | semidirect |
| 6. #11725445 | C2 | semidirect |
| 7. #11725444 | C2 | semidirect |
| 66. #2808 | D7 | semidirect |
| 421. C7 | #7746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2808 | 2 |
| #11727442 | 2 |
| #11727412 | 2 |
| #11727381 | 2 |
| #11725448 | 2 |
| #11725445 | 2 |
| #11725444 | 2 |
| #7746 | 7 |