Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
234 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 234 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. C7×D4×C16 | C2 | semidirect |
| 2. #11728607 | C2 | semidirect |
| 4. #11726812 | C2 | semidirect |
| 5. #11725371 | C2 | semidirect |
| 6. #11725366 | C2 | semidirect |
| 7. #11725307 | C2 | semidirect |
| 46. D4×C16 | D7 | semidirect |
| 203. C7 | #12468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×D4×C16 | 2 |
| #11728607 | 2 |
| #11728601 | 2 |
| #11726812 | 2 |
| #11725371 | 2 |
| #11725366 | 2 |
| #11725307 | 2 |
| #12468 | 7 |