Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
250 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 3. C7×#1370 | C2 | semidirect |
| 4. #11725360 | C2 | semidirect |
| 5. #11725246 | C2 | semidirect |
| 40. #1370 | D7 | semidirect |
| 184. C7 | #12013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11727029 | 2 |
| C82×D7 | 2 |
| C7×#1370 | 2 |
| #11725360 | 2 |
| #11725246 | 2 |
| #12013 | 7 |