Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
324 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 324 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. #11728606 | C2 | semidirect |
| 3. #11727043 | C2 | semidirect |
| 4. #11726798 | C2 | semidirect |
| 5. C7×D4⋊C16 | C2 | semidirect |
| 6. #11725370 | C2 | semidirect |
| 7. #11725310 | C2 | semidirect |
| 59. D4⋊C16 | D7 | semidirect |
| 245. C7 | #12392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736856 | 2 |
| #11728606 | 2 |
| #11727043 | 2 |
| #11726798 | 2 |
| C7×D4⋊C16 | 2 |
| #11725370 | 2 |
| #11725310 | 2 |
| #12392 | 7 |