Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
598 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 1. #11740423 | C2 | semidirect |
| 3. #11735983 | C2 | semidirect |
| 4. C7×#1527 | C2 | semidirect |
| 5. #11728586 | C2 | semidirect |
| 6. #11728578 | C2 | semidirect |
| 7. #11725471 | C2 | semidirect |
| 81. #1527 | D7 | semidirect |
| 353. C7 | #10090 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740423 | 2 |
| #11740392 | 2 |
| #11735983 | 2 |
| C7×#1527 | 2 |
| #11728586 | 2 |
| #11728578 | 2 |
| #11725471 | 2 |
| #10090 | 7 |