Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
294 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. D7×M64 | C2 | semidirect |
| 3. #11727099 | C2 | semidirect |
| 4. C7×#1418 | C2 | semidirect |
| 5. #11725634 | C2 | semidirect |
| 6. #11725412 | C2 | semidirect |
| 7. #11725386 | C2 | semidirect |
| 11. #89691 | C4 | semidirect |
| 12. D7×Q32 | C4 | semidirect |
| 15. #89684 | C4 | semidirect |
| 16. D7×D16 | C4 | semidirect |
| 20. C7×M64 | C22 | semidirect |
| 21. C7×#367 | C22 | semidirect |
| 22. #89300 | C22 | semidirect |
| 23. #89294 | C22 | semidirect |
| 67. #1418 | D7 | semidirect |
| 117. M64 | C2×D7 | semidirect |
| 120. #367 | C2×D7 | semidirect |
| 269. C7 | #13622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D7×#508 | 2 |
| D7×M64 | 2 |
| #11727099 | 2 |
| C7×#1418 | 2 |
| #11725634 | 2 |
| #11725412 | 2 |
| #11725386 | 2 |
| #13622 | 7 |