Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2186 conjugacy classes of subgroups; only the 683 normal subgroups are shown.
This group has 2186 conjugacy classes of subgroups — too many to draw. Only its 683 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×C43×C7 | C2 | semidirect |
| 3. C2×#89705 | C2 | semidirect |
| 4. #11730761 | C2 | direct (N × H) |
| 8. C43×C7 | C22 | semidirect |
| 11. #89705 | C22 | semidirect |
| 26. C2×C43 | D7 | semidirect |
| 45. C43 | C2×D7 | semidirect |
| 84. C2×C7 | #2865 | semidirect |
| 97. C7 | C2×#2865 | semidirect |
| 105. C2 | #11730761 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C43×C7 | 2 |
| C2×#89712 | 2 |
| C2×#89705 | 2 |
| #11730761 | 2 |
| C2×#2865 | 7 |