Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
670 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 267 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 |
|---|---|---|
| 4. #11729250 | C2 | direct (N × H) |
| 9. C2×C7×Q32 | C4 | semidirect |
| 35. C7×Q32 | C2×C4 | semidirect |
| 78. C2×Q32 | Dic7 | semidirect |
| 121. Q32 | C2×Dic7 | semidirect |
| 165. C2×C7 | #2176 | semidirect |
| 186. C7 | C2×#2176 | semidirect |
| 196. C2 | #11729250 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×Q32 | 2 |
| C2×Q16×Dic7 | 2 |
| C2×#89359 | 2 |
| #11729250 | 2 |
| C2×#89300 | 2 |
| C2×#89297 | 2 |
| C2×#2176 | 7 |