Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1062 conjugacy classes of subgroups; only the 411 normal subgroups are shown.
This group has 1062 conjugacy classes of subgroups — too many to draw. Only its 411 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 |
|---|---|---|
| 3. #11727147 | C2 | semidirect |
| 34. C42×C7 | M16 | semidirect |
| 83. C42 | #1136 | semidirect |
| 98. C7 | #20772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C43×C7 | 2 |
| #11729281 | 2 |
| #11727147 | 2 |
| #20772 | 7 |