Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
214 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 97 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×D7×C32 | C2 | semidirect |
| 3. C7×C4⋊C32 | C2 | semidirect |
| 4. (C2×D7)⋊C32 | C2 | semidirect |
| 5. C4×C7⋊C32 | C2 | semidirect |
| 28. C7⋊C32 | D4 | semidirect |
| 31. C4⋊C32 | D7 | semidirect |
| 62. D28 | C32 | semidirect |
| 85. C2×D7 | C2×C32 | semidirect |
| 87. C4×C7 | C2×C32 | semidirect |
| 121. C7 | D4×C32 | semidirect |
| 128. C4 | D7×C32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×C32 | 2 |
| C16×D28 | 2 |
| C7×C4⋊C32 | 2 |
| (C2×D7)⋊C32 | 2 |
| C4×C7⋊C32 | 2 |
| D4×C32 | 7 |