Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
522 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11741342 | C2 | semidirect |
| 3. C2×#89361 | C2 | semidirect |
| 4. #11729793 | C2 | semidirect |
| 5. #11729787 | C2 | semidirect |
| 6. #11725625 | C2 | semidirect |
| 7. #11725618 | C2 | semidirect |
| 12. C7×#509 | C4 | semidirect |
| 42. C2×C7×D8 | C2×C4 | semidirect |
| 58. C7×M32 | C2×C4 | semidirect |
| 99. C7×Q16 | C22⋊C4 | semidirect |
| 107. C7×D8 | C22⋊C4 | semidirect |
| 134. #509 | Dic7 | semidirect |
| 200. C2×D8 | C2×Dic7 | semidirect |
| 218. M32 | C2×Dic7 | semidirect |
| 269. Q16 | C22⋊Dic7 | semidirect |
| 277. D8 | C22⋊Dic7 | 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×C7×#509 | 2 |
| #11741342 | 2 |
| C2×#89361 | 2 |
| #11729793 | 2 |
| #11729787 | 2 |
| #11725625 | 2 |
| #11725618 | 2 |
| #13025 | 7 |