Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
522 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 107 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. #11736611 | C2 | semidirect |
| 3. C7×#2140 | C2 | semidirect |
| 4. #11729793 | C2 | semidirect |
| 5. C2×#89313 | C2 | semidirect |
| 6. #11725618 | C2 | semidirect |
| 7. #11725532 | C2 | semidirect |
| 17. #89919 | C4 | semidirect |
| 36. C2×C7×D8 | C2×C4 | semidirect |
| 68. #6386 | C2×C4 | semidirect |
| 75. #2140 | D7 | semidirect |
| 123. Dic28 | C22⋊C4 | semidirect |
| 125. D56 | C22⋊C4 | semidirect |
| 201. C2×D8 | C4×D7 | semidirect |
| 343. C7 | #13025 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89919 | 2 |
| #11736611 | 2 |
| C7×#2140 | 2 |
| #11729793 | 2 |
| C2×#89313 | 2 |
| #11725618 | 2 |
| #11725532 | 2 |
| #13025 | 7 |