Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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. #11727097 | C2 | semidirect |
| 3. C7×#1426 | C2 | semidirect |
| 5. #11725405 | C2 | semidirect |
| 6. #11725388 | C2 | semidirect |
| 39. #1426 | D7 | semidirect |
| 141. C7 | #13709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11727111 | 2 |
| #11727097 | 2 |
| C7×#1426 | 2 |
| #11725412 | 2 |
| #11725405 | 2 |
| #11725388 | 2 |
| #11725386 | 2 |
| #13709 | 7 |