Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
628 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 628 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 |
|---|---|---|
| 1. C7×#3234 | C2 | semidirect |
| 3. #11740512 | C2 | semidirect |
| 4. #11729566 | C2 | semidirect |
| 5. #11729489 | C2 | semidirect |
| 6. #11728572 | C2 | semidirect |
| 7. #11725554 | C2 | semidirect |
| 77. #3234 | D7 | semidirect |
| 351. C7 | #10089 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3234 | 2 |
| #11740732 | 2 |
| #11740512 | 2 |
| #11729566 | 2 |
| #11729489 | 2 |
| #11728572 | 2 |
| #11725554 | 2 |
| #10089 | 7 |