Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
446 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 83 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. C7×#1484 | C2 | semidirect |
| 3. #11729564 | C2 | semidirect |
| 4. #11728528 | C2 | semidirect |
| 5. #11728507 | C2 | semidirect |
| 6. #11727630 | C2 | semidirect |
| 7. #11725475 | C2 | semidirect |
| 70. #1484 | D7 | semidirect |
| 318. C7 | #10488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740747 | 2 |
| C7×#1484 | 2 |
| #11729564 | 2 |
| #11728528 | 2 |
| #11728507 | 2 |
| #11727630 | 2 |
| #11725475 | 2 |
| #10488 | 7 |