Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
542 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 542 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 |
|---|---|---|
| 3. #11740697 | C2 | semidirect |
| 5. #11729529 | C2 | semidirect |
| 6. #11728534 | C2 | semidirect |
| 7. #11725542 | C2 | semidirect |
| 319. C7 | #10285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3227 | 2 |
| #11740716 | 2 |
| #11740697 | 2 |
| #11729569 | 2 |
| #11729529 | 2 |
| #11728534 | 2 |
| #11725542 | 2 |
| #10285 | 7 |