Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
626 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #11730756 | C2 | semidirect |
| 4. #11728534 | C2 | semidirect |
| 5. #11728533 | C2 | semidirect |
| 7. C7×#1276 | C2 | semidirect |
| 78. #1276 | D7 | semidirect |
| 104. C42×C7 | SD16 | semidirect |
| 281. C42 | #1132 | semidirect |
| 325. C7 | #10283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736757 | 2 |
| #11736714 | 2 |
| #11730756 | 2 |
| #11728534 | 2 |
| #11728533 | 2 |
| #11727149 | 2 |
| C7×#1276 | 2 |
| #10283 | 7 |