Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
408 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 97 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×#89362 | C2 | semidirect |
| 3. #11729832 | C2 | semidirect |
| 4. #11729770 | C2 | semidirect |
| 5. C2×#89356 | C2 | semidirect |
| 6. C2×#89284 | C2 | semidirect |
| 7. #11725529 | C2 | semidirect |
| 68. C2×C7⋊C16 | D4 | semidirect |
| 340. C7 | #13384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3061 | 2 |
| C2×#89362 | 2 |
| #11729832 | 2 |
| #11729770 | 2 |
| C2×#89356 | 2 |
| C2×#89284 | 2 |
| #11725529 | 2 |
| #13384 | 7 |