Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
662 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 119 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. #11740402 | C2 | semidirect |
| 3. #11729519 | C2 | semidirect |
| 4. C2×#89335 | C2 | semidirect |
| 5. #11725465 | C2 | semidirect |
| 11. C7×#496 | C4 | semidirect |
| 37. C7×#127 | C2×C4 | semidirect |
| 51. C7×#97 | C2×C4 | semidirect |
| 117. #496 | Dic7 | semidirect |
| 186. #127 | C2×Dic7 | semidirect |
| 203. #97 | C2×Dic7 | semidirect |
| 327. C7 | #9001 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#496 | 2 |
| #11740402 | 2 |
| #11729519 | 2 |
| C2×#89335 | 2 |
| #11725465 | 2 |
| #9001 | 7 |