Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
398 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 77 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×#2605 | C2 | semidirect |
| 5. #11725439 | C2 | semidirect |
| 6. #11725427 | C2 | semidirect |
| 7. #11725421 | C2 | semidirect |
| 42. #6437 | Q8 | semidirect |
| 45. #6432 | Q8 | semidirect |
| 68. #2605 | D7 | semidirect |
| 335. C7 | #10378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2605 | 2 |
| #11727318 | 2 |
| #11727246 | 2 |
| #11727186 | 2 |
| #11725439 | 2 |
| #11725427 | 2 |
| #11725421 | 2 |
| #10378 | 7 |