Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#89679 | C2 | semidirect |
| 3. #11729204 | C2 | semidirect |
| 4. #11728473 | C2 | semidirect |
| 5. C2×#89292 | C2 | semidirect |
| 6. C7×#1388 | C2 | semidirect |
| 7. #11725535 | C2 | semidirect |
| 23. #89669 | C4 | semidirect |
| 24. #89668 | C4 | semidirect |
| 78. #1388 | D7 | semidirect |
| 339. C7 | #13071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89679 | 2 |
| #11736701 | 2 |
| #11729204 | 2 |
| #11728473 | 2 |
| C2×#89292 | 2 |
| C7×#1388 | 2 |
| #11725535 | 2 |
| #13071 | 7 |