Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
506 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 165 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. #11737359 | C2 | semidirect |
| 3. C7×Q8×C16 | C2 | semidirect |
| 4. #11727049 | C2 | semidirect |
| 6. #11726819 | C2 | semidirect |
| 52. Q8×C16 | D7 | semidirect |
| 96. C7×Q8 | SD32 | semidirect |
| 178. Q8 | #6374 | semidirect |
| 191. C7 | #33926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D56 | 2 |
| #11737359 | 2 |
| C7×Q8×C16 | 2 |
| #11727049 | 2 |
| #11727041 | 2 |
| #11726819 | 2 |
| C4×#6374 | 2 |
| #33926 | 7 |