Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
216 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 57 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. #11727127 | C2 | semidirect |
| 2. #11726821 | C2 | semidirect |
| 3. #11726814 | C2 | semidirect |
| 4. C7×#1422 | C2 | semidirect |
| 5. #11725410 | C2 | semidirect |
| 28. Dic56 | D4 | semidirect |
| 33. D112 | D4 | semidirect |
| 38. #1422 | D7 | semidirect |
| 148. C7 | #13692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11727127 | 2 |
| #11726821 | 2 |
| #11726814 | 2 |
| C7×#1422 | 2 |
| #11725410 | 2 |
| #13692 | 7 |