Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
398 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 117. C7⋊C8 | #101 | semidirect |
| 212. C7 | #8615 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C7⋊C8 | 2 |
| C7×#1801 | 2 |
| #11729391 | 2 |
| #11728244 | 2 |
| #11725517 | 2 |
| #8615 | 7 |