Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
4990 conjugacy classes of subgroups; only the 1771 normal subgroups are shown.
This group has 4990 conjugacy classes of subgroups — too many to draw. Only its 1771 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. C22×#6410 | C2 | direct (N × H) |
| 13. C2×#6410 | C22 | direct (N × H) |
| 32. #6410 | C23 | direct (N × H) |
| 70. C23×C7 | #101 | semidirect |
| 106. C22×C7 | C2×#101 | semidirect |
| 137. C2×C7 | C22×#101 | semidirect |
| 141. C23 | #6410 | direct (N × H) |
| 157. C7 | C23×#101 | semidirect |
| 160. C22 | C2×#6410 | direct (N × H) |
| 169. C2 | C22×#6410 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C7×Q8 | 2 |
| C23×#1136 | 2 |
| C22×#6410 | 2 |
| C23×#101 | 7 |