Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
234 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 69 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×#1675 | C2 | semidirect |
| 2. #11729135 | C2 | semidirect |
| 3. D4×C7⋊C16 | C2 | semidirect |
| 5. #11725608 | C2 | semidirect |
| 6. #11725279 | C2 | semidirect |
| 7. #11725276 | C2 | semidirect |
| 47. #1675 | 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×#1675 | 2 |
| #11729135 | 2 |
| D4×C7⋊C16 | 2 |
| #11728601 | 2 |
| #11725608 | 2 |
| #11725279 | 2 |
| #11725276 | 2 |
| #12468 | 7 |