Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
316 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 316 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. #11728832 | C2 | semidirect |
| 4. #11728216 | C2 | semidirect |
| 5. #11725582 | C2 | semidirect |
| 7. #11725515 | C2 | semidirect |
| 280. C7 | #12290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3250 | 2 |
| #11728832 | 2 |
| #11728822 | 2 |
| #11728216 | 2 |
| #11725582 | 2 |
| #11725580 | 2 |
| #11725515 | 2 |
| #12290 | 7 |