Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
324 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 67 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. #11728640 | C2 | semidirect |
| 3. #11726798 | C2 | semidirect |
| 4. #11726332 | C2 | semidirect |
| 5. C7×#1331 | C2 | semidirect |
| 6. #11725309 | C2 | semidirect |
| 7. #11725281 | C2 | semidirect |
| 58. #1331 | D7 | semidirect |
| 245. C7 | #12392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11737059 | 2 |
| #11728640 | 2 |
| #11726798 | 2 |
| #11726332 | 2 |
| C7×#1331 | 2 |
| #11725309 | 2 |
| #11725281 | 2 |
| #12392 | 7 |