Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
180 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 91 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×#1397 | C2 | semidirect |
| 4. Dic7⋊C32 | C2 | semidirect |
| 5. C4×C7⋊C32 | C2 | semidirect |
| 34. #1397 | D7 | semidirect |
| 127. C7 | #13641 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11726805 | 2 |
| C7×#1397 | 2 |
| (C2×D7)⋊C32 | 2 |
| Dic7⋊C32 | 2 |
| C4×C7⋊C32 | 2 |
| #13641 | 7 |