Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1482 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 1482 conjugacy classes of subgroups — too many to draw. Only its 227 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. C2×#89320 | C2 | semidirect |
| 3. #11729285 | C2 | semidirect |
| 20. C22×C7×D4 | C8 | semidirect |
| 140. C22×D4 | C7⋊C8 | semidirect |
| 275. C7 | #8302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C7×D4 | 2 |
| C2×#89320 | 2 |
| #11729285 | 2 |
| #8302 | 7 |