Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
206 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 181. C7 | #12450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×C8×Q16 | 2 |
| #11728665 | 2 |
| #11728664 | 2 |
| #11725818 | 2 |
| #11725282 | 2 |
| #11725281 | 2 |
| #11725246 | 2 |
| #12450 | 7 |