Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
712 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 1. C2×#89856 | C2 | semidirect |
| 3. C7×#1956 | C2 | semidirect |
| 4. C2×#89254 | C2 | semidirect |
| 5. #11725440 | C2 | semidirect |
| 28. C7×C4⋊Q8 | D4 | semidirect |
| 49. C4⋊(C7⋊C8) | D4 | semidirect |
| 52. #1956 | D7 | semidirect |
| 159. C4⋊Q8 | D28 | semidirect |
| 289. C7 | #10235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89856 | 2 |
| #11731813 | 2 |
| C7×#1956 | 2 |
| C2×#89254 | 2 |
| #11725440 | 2 |
| #10235 | 7 |