Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
180 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 87 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×C4⋊C32 | C2 | semidirect |
| 5. #11725395 | C2 | semidirect |
| 6. Dic7×C32 | C2 | semidirect |
| 7. C4⋊(C7⋊C32) | C2 | semidirect |
| 40. C4⋊C32 | D7 | semidirect |
| 155. 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×C4⋊C32 | 2 |
| (C2×D7)⋊C32 | 2 |
| #11725395 | 2 |
| Dic7×C32 | 2 |
| C4⋊(C7⋊C32) | 2 |
| #13641 | 7 |