Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
480 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 89 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. #11736787 | C2 | semidirect |
| 3. C7×#1555 | C2 | semidirect |
| 4. #11729520 | C2 | semidirect |
| 5. #11728559 | C2 | semidirect |
| 6. #11725564 | C2 | semidirect |
| 7. #11725559 | C2 | semidirect |
| 86. #1555 | D7 | semidirect |
| 376. C7 | #9340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740612 | 2 |
| #11736787 | 2 |
| C7×#1555 | 2 |
| #11729520 | 2 |
| #11728559 | 2 |
| #11725564 | 2 |
| #11725559 | 2 |
| #9340 | 7 |