Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
310 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 310 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 |
|---|---|---|
| 39. C7×M32 | Q8 | semidirect |
| 42. C7×#108 | Q8 | semidirect |
| 55. C2×C7⋊C16 | Q8 | semidirect |
| 149. M32 | Dic14 | semidirect |
| 156. #108 | Dic14 | semidirect |
| 234. C7 | #13460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736617 | 2 |
| C2×#89308 | 2 |
| #11728461 | 2 |
| #11728404 | 2 |
| C7×#1389 | 2 |
| #11725620 | 2 |
| #11725536 | 2 |
| #13460 | 7 |