Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1006 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 1006 conjugacy classes of subgroups — too many to draw. Only its 459 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 |
|---|---|---|
| 27. C4×C7×C8 | Q8 | semidirect |
| 71. C7×C8 | C4⋊Q8 | semidirect |
| 84. C4×C8 | Dic14 | semidirect |
| 92. C4×C7 | #500 | semidirect |
| 128. C8 | #6432 | semidirect |
| 129. C7 | #33312 | semidirect |
| 135. C4 | #89454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89454 | 2 |
| #11730756 | 2 |
| C42×C7×C8 | 2 |
| #11727519 | 2 |
| #33312 | 7 |