Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
432 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 97 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. #11729832 | C2 | semidirect |
| 3. C2×#89361 | C2 | semidirect |
| 4. #11729742 | C2 | semidirect |
| 5. C2×#89348 | C2 | semidirect |
| 6. #11728403 | C2 | semidirect |
| 7. #11725532 | C2 | semidirect |
| 74. #6386 | D4 | semidirect |
| 384. C7 | #13386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3054 | 2 |
| #11729832 | 2 |
| C2×#89361 | 2 |
| #11729742 | 2 |
| C2×#89348 | 2 |
| #11728403 | 2 |
| #11725532 | 2 |
| #13386 | 7 |