Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
486 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 87 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. #11727029 | C2 | semidirect |
| 3. #11726324 | C2 | semidirect |
| 4. C7×#1361 | C2 | semidirect |
| 5. #11725596 | C2 | semidirect |
| 6. #11725366 | C2 | semidirect |
| 7. #11725279 | C2 | semidirect |
| 18. C7×C4⋊C16 | C22 | semidirect |
| 19. C7×#335 | C22 | semidirect |
| 23. C4⋊(C7⋊C16) | C22 | semidirect |
| 24. #89253 | C22 | semidirect |
| 62. #1361 | D7 | semidirect |
| 115. C4⋊C16 | C2×D7 | semidirect |
| 119. #335 | C2×D7 | semidirect |
| 291. C7 | #11964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D7×#493 | 2 |
| #11727029 | 2 |
| #11726324 | 2 |
| C7×#1361 | 2 |
| #11725596 | 2 |
| #11725366 | 2 |
| #11725279 | 2 |
| #11964 | 7 |