Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
626 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11736731 | C2 | semidirect |
| 3. C7×#1486 | C2 | semidirect |
| 4. #11729352 | C2 | semidirect |
| 5. #11728281 | C2 | semidirect |
| 6. #11725544 | C2 | semidirect |
| 7. #11725519 | C2 | semidirect |
| 58. C4×C7×C8 | D4 | semidirect |
| 68. C4×C7⋊C8 | D4 | semidirect |
| 73. #1486 | D7 | semidirect |
| 238. C4×C8 | C22⋊D7 | semidirect |
| 383. C7 | #9485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739860 | 2 |
| #11736731 | 2 |
| C7×#1486 | 2 |
| #11729352 | 2 |
| #11728281 | 2 |
| #11725544 | 2 |
| #11725519 | 2 |
| #9485 | 7 |