Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1010 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1010 conjugacy classes of subgroups — too many to draw. Only its 187 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×#563 | C2 | semidirect |
| 2. C2×#89839 | C2 | semidirect |
| 4. #11729709 | C2 | direct (N × H) |
| 5. C2×#89338 | C2 | semidirect |
| 6. C2×#89335 | C2 | semidirect |
| 9. C7×#563 | C22 | semidirect |
| 20. #89839 | C22 | semidirect |
| 27. #89338 | C22 | semidirect |
| 28. #89335 | C22 | semidirect |
| 76. C2×#563 | D7 | semidirect |
| 133. #563 | C2×D7 | semidirect |
| 293. C2×C7 | #1657 | semidirect |
| 329. C7 | C2×#1657 | semidirect |
| 348. C2 | #11729709 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#563 | 2 |
| C2×#89839 | 2 |
| C2×#89830 | 2 |
| #11729709 | 2 |
| C2×#89338 | 2 |
| C2×#89335 | 2 |
| C2×#1657 | 7 |