Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
176 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 57 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. #11727074 | C2 | semidirect |
| 3. C7×#1424 | C2 | semidirect |
| 5. Dic7⋊C32 | C2 | semidirect |
| 7. #11725382 | C2 | semidirect |
| 32. D112 | Q8 | semidirect |
| 38. #1424 | D7 | semidirect |
| 143. C7 | #13705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11727074 | 2 |
| #11727071 | 2 |
| C7×#1424 | 2 |
| #11725402 | 2 |
| Dic7⋊C32 | 2 |
| #11725383 | 2 |
| #11725382 | 2 |
| #13705 | 7 |