Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
420 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. C7×#1805 | C2 | semidirect |
| 3. #11729378 | C2 | semidirect |
| 5. #11728176 | C2 | semidirect |
| 7. #11725437 | C2 | semidirect |
| 68. #1805 | D7 | semidirect |
| 336. C7 | #10466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739886 | 2 |
| C7×#1805 | 2 |
| #11729378 | 2 |
| #11728185 | 2 |
| #11728176 | 2 |
| #11727299 | 2 |
| #11725437 | 2 |
| #10466 | 7 |