Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 67 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. #11729028 | C2 | semidirect |
| 3. #11728641 | C2 | semidirect |
| 4. D8×C7⋊C8 | C2 | semidirect |
| 5. #11725596 | C2 | semidirect |
| 6. #11725371 | C2 | semidirect |
| 7. #11725360 | C2 | semidirect |
| 63. C7×D8 | SD16 | semidirect |
| 165. D8 | #1142 | semidirect |
| 209. C7 | #12418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2206 | 2 |
| #11729028 | 2 |
| #11728641 | 2 |
| D8×C7⋊C8 | 2 |
| #11725596 | 2 |
| #11725371 | 2 |
| #11725360 | 2 |
| #12418 | 7 |