Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
370 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 22. C2×C7×Q16 | Q8 | semidirect |
| 116. C2×Q16 | Dic14 | semidirect |
| 206. C7 | #13368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11735924 | 2 |
| C7×#1971 | 2 |
| #11729815 | 2 |
| #11725527 | 2 |
| #11725470 | 2 |
| #13368 | 7 |