Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
808 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×C7×#564 | C2 | semidirect |
| 4. #11729715 | C2 | semidirect |
| 5. #11729714 | C2 | semidirect |
| 6. #11729490 | C2 | semidirect |
| 7. #11729489 | C2 | semidirect |
| 73. C2×#564 | D7 | semidirect |
| 275. C7 | #19003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#564 | 2 |
| #11740464 | 2 |
| #11740457 | 2 |
| #11729715 | 2 |
| #11729714 | 2 |
| #11729490 | 2 |
| #11729489 | 2 |
| #19003 | 7 |