Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
284 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 2. C2×#89317 | C2 | semidirect |
| 4. #11725632 | C2 | semidirect |
| 110. C22×C7 | Q64 | semidirect |
| 160. C7 | #13665 | semidirect |
| 163. C22 | #89317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×Q32 | 2 |
| C2×#89317 | 2 |
| #11729170 | 2 |
| #11725632 | 2 |
| C22⋊(C7⋊C32) | 2 |
| #13665 | 7 |