Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
462 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 97. C2×C7×C8 | Q16 | semidirect |
| 256. C2×C8 | #1144 | semidirect |
| 316. C7 | #10224 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3162 | 2 |
| #11740815 | 2 |
| #11740769 | 2 |
| #11729592 | 2 |
| #11727582 | 2 |
| #11725467 | 2 |
| #10224 | 7 |