Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
540 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×C7×#361 | C2 | semidirect |
| 3. #11729787 | C2 | semidirect |
| 4. #11729194 | C2 | semidirect |
| 5. #11728458 | C2 | semidirect |
| 6. C2×#89290 | C2 | semidirect |
| 7. #11725616 | C2 | semidirect |
| 56. #6392 | D4 | semidirect |
| 66. C2×#361 | D7 | semidirect |
| 308. C7 | #13413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89923 | 2 |
| C2×C7×#361 | 2 |
| #11729787 | 2 |
| #11729194 | 2 |
| #11728458 | 2 |
| C2×#89290 | 2 |
| #11725616 | 2 |
| #13413 | 7 |