Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
814 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 814 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 |
|---|---|---|
| 5. #11729253 | C2 | direct (N × H) |
| 115. C2×Dic7 | Q32 | semidirect |
| 159. Dic7 | C2×Q32 | semidirect |
| 190. C2×C7 | #2247 | semidirect |
| 214. C7 | C2×#2247 | semidirect |
| 224. C2 | #11729253 | 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×#89953 | 2 |
| C22×#6403 | 2 |
| C22×Dic56 | 2 |
| #11729253 | 2 |
| C2×C16×Dic7 | 2 |
| C2×#2247 | 7 |