Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
570 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 99 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. #11740762 | C2 | semidirect |
| 3. #11736714 | C2 | semidirect |
| 4. C7×#1517 | C2 | semidirect |
| 5. #11727309 | C2 | semidirect |
| 6. #11727299 | C2 | semidirect |
| 7. #11725547 | C2 | semidirect |
| 83. #1517 | D7 | semidirect |
| 135. C2×C7⋊C8 | SD16 | semidirect |
| 362. C7 | #10221 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740762 | 2 |
| #11740731 | 2 |
| #11736714 | 2 |
| C7×#1517 | 2 |
| #11727309 | 2 |
| #11727299 | 2 |
| #11725547 | 2 |
| #10221 | 7 |