Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
304 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 69 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. #11739401 | C2 | semidirect |
| 5. C7×#1365 | C2 | semidirect |
| 6. #11725364 | C2 | semidirect |
| 7. #11725278 | C2 | semidirect |
| 58. #1365 | D7 | semidirect |
| 85. Dic28 | SD16 | semidirect |
| 128. Dic14 | SD32 | semidirect |
| 236. C7 | #12354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739401 | 2 |
| #11729135 | 2 |
| #11727046 | 2 |
| #11726340 | 2 |
| C7×#1365 | 2 |
| #11725364 | 2 |
| #11725278 | 2 |
| #12354 | 7 |