Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
284 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 61 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×C7×Q64 | C2 | semidirect |
| 4. C2×#89317 | C2 | semidirect |
| 5. #11725632 | C2 | semidirect |
| 6. #11725403 | C2 | semidirect |
| 50. C2×Q64 | D7 | semidirect |
| 142. C2×D7 | Q64 | semidirect |
| 199. C7 | #13665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×Q32 | 2 |
| C2×C7×Q64 | 2 |
| #11729258 | 2 |
| C2×#89317 | 2 |
| #11725632 | 2 |
| #11725403 | 2 |
| (C2×D7)⋊C32 | 2 |
| #13665 | 7 |