Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
274 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 274 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 |
|---|---|---|
| 1. #11727046 | C2 | semidirect |
| 3. C8×Dic28 | C2 | semidirect |
| 4. C7×#1370 | C2 | semidirect |
| 5. #11725366 | C2 | semidirect |
| 39. #1370 | D7 | semidirect |
| 56. Dic28 | D8 | semidirect |
| 91. C7×C8 | SD32 | semidirect |
| 168. C8 | #6374 | semidirect |
| 171. C7 | #12425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11727046 | 2 |
| #11725816 | 2 |
| C8×Dic28 | 2 |
| C7×#1370 | 2 |
| #11725366 | 2 |
| #12425 | 7 |