Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
318 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 48. #6393 | Q8 | semidirect |
| 52. #6386 | Q8 | semidirect |
| 56. C2×C7⋊C16 | Q8 | semidirect |
| 246. C7 | #13456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3164 | 2 |
| #11728403 | 2 |
| C2×#89285 | 2 |
| #11727648 | 2 |
| #11725530 | 2 |
| #11725529 | 2 |
| #11725477 | 2 |
| #13456 | 7 |