Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
798 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 211 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×#3160 | C2 | semidirect |
| 2. #11740788 | C2 | semidirect |
| 4. #11729117 | C2 | semidirect |
| 5. #11729092 | C2 | semidirect |
| 6. #11729090 | C2 | semidirect |
| 7. C2×#89250 | C2 | semidirect |
| 60. #3160 | D7 | semidirect |
| 75. C2×C7×C8 | SD16 | semidirect |
| 189. C2×C8 | #1143 | semidirect |
| 225. C7 | #19608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3160 | 2 |
| #11740788 | 2 |
| #11735912 | 2 |
| #11729117 | 2 |
| #11729092 | 2 |
| #11729090 | 2 |
| C2×#89250 | 2 |
| #19608 | 7 |