Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
712 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 137 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×#89780 | C2 | semidirect |
| 3. C2×D4⋊(C7⋊C8) | C2 | semidirect |
| 4. #11727333 | C2 | semidirect |
| 5. #11725440 | C2 | semidirect |
| 42. #6432 | D4 | semidirect |
| 48. C4⋊(C7⋊C8) | D4 | semidirect |
| 289. C7 | #10235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2537 | 2 |
| C2×#89780 | 2 |
| C2×D4⋊(C7⋊C8) | 2 |
| #11727333 | 2 |
| #11725440 | 2 |
| #10235 | 7 |