Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
176 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 65 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. C7×#2252 | C2 | semidirect |
| 4. #11725382 | C2 | semidirect |
| 5. C4⋊(C7⋊C32) | C2 | semidirect |
| 27. D112 | Q8 | semidirect |
| 29. #2252 | D7 | semidirect |
| 126. C7 | #13705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2252 | 2 |
| C4×D112 | 2 |
| #11725383 | 2 |
| #11725382 | 2 |
| C4⋊(C7⋊C32) | 2 |
| #13705 | 7 |