Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
364 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 364 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. #11726847 | C2 | semidirect |
| 3. #11726670 | C2 | semidirect |
| 4. C7×#1349 | C2 | semidirect |
| 5. #11725581 | C2 | semidirect |
| 6. #11725333 | C2 | semidirect |
| 7. #11725293 | C2 | semidirect |
| 68. #1349 | D7 | semidirect |
| 293. C7 | #11751 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11738142 | 2 |
| #11726847 | 2 |
| #11726670 | 2 |
| C7×#1349 | 2 |
| #11725581 | 2 |
| #11725333 | 2 |
| #11725293 | 2 |
| #11751 | 7 |