Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
478 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 105 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. C7×#1546 | C2 | semidirect |
| 4. #11729527 | C2 | semidirect |
| 6. #11725544 | C2 | semidirect |
| 7. #11725519 | C2 | semidirect |
| 75. #1546 | D7 | semidirect |
| 359. C7 | #9196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740706 | 2 |
| #11736484 | 2 |
| C7×#1546 | 2 |
| #11729527 | 2 |
| #11728536 | 2 |
| #11725544 | 2 |
| #11725519 | 2 |
| #9196 | 7 |