Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
644 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 4. #11727221 | C2 | semidirect |
| 5. #11725425 | C2 | semidirect |
| 16. #89339 | C4 | semidirect |
| 41. C4⋊(C7⋊C8) | C2×C4 | semidirect |
| 251. C7 | #8924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2366 | 2 |
| #11729518 | 2 |
| C2×#89339 | 2 |
| #11727221 | 2 |
| #11725425 | 2 |
| #8924 | 7 |