Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1154 conjugacy classes of subgroups; only the 299 normal subgroups are shown.
This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 299 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×#89460 | C2 | semidirect |
| 3. C7×#1726 | C2 | semidirect |
| 4. #11727591 | C2 | semidirect |
| 5. #11727193 | C2 | semidirect |
| 29. C4×C7×C8 | D4 | semidirect |
| 37. #1726 | D7 | semidirect |
| 94. C4×C8 | D28 | semidirect |
| 140. C7 | #21684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89460 | 2 |
| #11730863 | 2 |
| C7×#1726 | 2 |
| #11727591 | 2 |
| #11727193 | 2 |
| #21684 | 7 |