Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
572 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 109 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. #11726357 | C2 | semidirect |
| 3. #11726350 | C2 | semidirect |
| 4. C7×#1270 | C2 | semidirect |
| 5. #11725445 | C2 | semidirect |
| 6. #11725285 | C2 | semidirect |
| 7. #11725285 | C2 | semidirect |
| 70. #1270 | D7 | semidirect |
| 410. C7 | #7679 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11733869 | 2 |
| #11726357 | 2 |
| #11726350 | 2 |
| C7×#1270 | 2 |
| #11725445 | 2 |
| #11725285 | 2 |
| #7679 | 7 |