Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
296 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 296 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 |
|---|---|---|
| 2. #11729136 | C2 | semidirect |
| 3. #11728696 | C2 | semidirect |
| 5. #11725608 | C2 | semidirect |
| 6. Q8⋊(C7⋊C16) | C2 | semidirect |
| 232. C7 | #12359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3380 | 2 |
| #11729136 | 2 |
| #11728696 | 2 |
| #11728646 | 2 |
| #11725608 | 2 |
| Q8⋊(C7⋊C16) | 2 |
| #11725569 | 2 |
| #12359 | 7 |