Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
678 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 107 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. #11740629 | C2 | semidirect |
| 3. #11736713 | C2 | semidirect |
| 4. C7×#1545 | C2 | semidirect |
| 5. #11728266 | C2 | semidirect |
| 6. #11728260 | C2 | semidirect |
| 7. #11725542 | C2 | semidirect |
| 78. #1545 | D7 | semidirect |
| 128. C4×Dic7 | D8 | semidirect |
| 355. C7 | #10284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740629 | 2 |
| #11740611 | 2 |
| #11736713 | 2 |
| C7×#1545 | 2 |
| #11728266 | 2 |
| #11728260 | 2 |
| #11725542 | 2 |
| #10284 | 7 |