Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 3. #11726311 | C2 | semidirect |
| 5. #11725311 | C2 | semidirect |
| 6. #11725305 | C2 | semidirect |
| 7. #11725276 | C2 | semidirect |
| 72. Dic28 | M16 | semidirect |
| 111. C7⋊C8 | SD32 | semidirect |
| 194. C7 | #12071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6401 | 2 |
| #11728635 | 2 |
| #11726311 | 2 |
| C7×#1331 | 2 |
| #11725311 | 2 |
| #11725305 | 2 |
| #11725276 | 2 |
| #12071 | 7 |