Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
414 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 105 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. #11727038 | C2 | semidirect |
| 3. #11726825 | C2 | semidirect |
| 4. C7×#1330 | C2 | semidirect |
| 5. #11725567 | C2 | semidirect |
| 6. #11725363 | C2 | semidirect |
| 7. #11725321 | C2 | semidirect |
| 21. C7×C4⋊C16 | C22 | semidirect |
| 22. C7×#346 | C22 | semidirect |
| 25. C4⋊(C7⋊C16) | C22 | semidirect |
| 26. #89256 | C22 | semidirect |
| 71. #1330 | D7 | semidirect |
| 133. C4⋊C16 | C2×D7 | semidirect |
| 135. #346 | C2×D7 | semidirect |
| 316. C7 | #11587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D7×#436 | 2 |
| #11727038 | 2 |
| #11726825 | 2 |
| C7×#1330 | 2 |
| #11725567 | 2 |
| #11725363 | 2 |
| #11725321 | 2 |
| #11587 | 7 |