Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
514 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 103 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. #11739654 | C2 | semidirect |
| 3. #11729353 | C2 | semidirect |
| 4. #11729326 | C2 | semidirect |
| 5. #11725439 | C2 | semidirect |
| 60. C4×C7⋊C8 | D4 | semidirect |
| 330. C7 | #9494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2598 | 2 |
| #11739654 | 2 |
| #11729353 | 2 |
| #11729326 | 2 |
| #11725439 | 2 |
| #9494 | 7 |