Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1010 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1010 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 6. #11726259 | C2 | direct (N × H) |
| 88. C2×Dic14 | Q16 | semidirect |
| 153. Dic14 | C2×Q16 | semidirect |
| 244. C2×C7 | #1633 | semidirect |
| 273. C7 | C2×#1633 | semidirect |
| 286. C2 | #11726259 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90413 | 2 |
| C2×#89864 | 2 |
| C2×#89622 | 2 |
| C2×C7×#333 | 2 |
| C2×#89279 | 2 |
| #11726259 | 2 |
| C2×#1633 | 7 |