Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
338 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 2. C7×#1676 | C2 | semidirect |
| 3. #11729142 | C2 | semidirect |
| 4. #11729135 | C2 | semidirect |
| 5. Q8⋊(C7⋊C16) | C2 | semidirect |
| 6. #11725279 | C2 | semidirect |
| 7. #11725277 | C2 | semidirect |
| 56. #1676 | D7 | semidirect |
| 249. C7 | #12384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11737355 | 2 |
| C7×#1676 | 2 |
| #11729142 | 2 |
| #11729135 | 2 |
| Q8⋊(C7⋊C16) | 2 |
| #11725279 | 2 |
| #11725277 | 2 |
| #12384 | 7 |