Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
558 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11728532 | C2 | semidirect |
| 5. #11728260 | C2 | semidirect |
| 6. C7×#1303 | C2 | semidirect |
| 7. #11725426 | C2 | semidirect |
| 71. #1303 | D7 | semidirect |
| 329. C7 | #9393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736731 | 2 |
| #11731247 | 2 |
| #11728532 | 2 |
| #11728281 | 2 |
| #11728260 | 2 |
| C7×#1303 | 2 |
| #11725426 | 2 |
| #9393 | 7 |