Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
590 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 1. C2×#89852 | C2 | semidirect |
| 4. C7×#1993 | C2 | semidirect |
| 5. C2×#89260 | C2 | semidirect |
| 7. #11725436 | C2 | semidirect |
| 81. #1993 | D7 | semidirect |
| 361. C7 | #10082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89852 | 2 |
| C2×#89858 | 2 |
| #11731700 | 2 |
| C7×#1993 | 2 |
| C2×#89260 | 2 |
| C2×#89259 | 2 |
| #11725436 | 2 |
| #10082 | 7 |