Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
416 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 79 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. #11729573 | C2 | semidirect |
| 3. #11725598 | C2 | semidirect |
| 4. #11725594 | C2 | semidirect |
| 6. C7×#532 | C4 | semidirect |
| 9. C7×#494 | C4 | semidirect |
| 11. C7×#492 | C4 | semidirect |
| 13. C2×C4×C7×C8 | C4 | semidirect |
| 83. #532 | Dic7 | semidirect |
| 86. #494 | Dic7 | semidirect |
| 88. #492 | Dic7 | semidirect |
| 91. C2×C4×C8 | Dic7 | semidirect |
| 228. C7 | #13583 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3147 | 2 |
| #11729573 | 2 |
| #11725598 | 2 |
| #11725594 | 2 |
| #13583 | 7 |