Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
406 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11727028 | C2 | semidirect |
| 3. #11726284 | C2 | semidirect |
| 4. C7×#1360 | C2 | semidirect |
| 5. #11725602 | C2 | semidirect |
| 6. #11725368 | C2 | semidirect |
| 7. #11725273 | C2 | semidirect |
| 20. C7×C4⋊C16 | C22 | semidirect |
| 21. C7×#334 | C22 | semidirect |
| 25. C4⋊(C7⋊C16) | C22 | semidirect |
| 26. #89252 | C22 | semidirect |
| 71. #1360 | D7 | semidirect |
| 135. C4⋊C16 | C2×D7 | semidirect |
| 140. #334 | C2×D7 | semidirect |
| 326. C7 | #11957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D7×#495 | 2 |
| #11727028 | 2 |
| #11726284 | 2 |
| C7×#1360 | 2 |
| #11725602 | 2 |
| #11725368 | 2 |
| #11725273 | 2 |
| #11957 | 7 |