Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
366 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #11729544 | C2 | semidirect |
| 5. #11729527 | C2 | semidirect |
| 6. #11728502 | C2 | semidirect |
| 7. #11725549 | C2 | semidirect |
| 288. C7 | #10491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3227 | 2 |
| #11729564 | 2 |
| #11729555 | 2 |
| #11729544 | 2 |
| #11729527 | 2 |
| #11728502 | 2 |
| #11725549 | 2 |
| #10491 | 7 |