Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
424 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 4. #11728379 | C2 | semidirect |
| 5. #11728350 | C2 | semidirect |
| 6. #11725613 | C2 | semidirect |
| 7. #11725611 | C2 | semidirect |
| 22. #89358 | C4 | semidirect |
| 53. #6393 | C2×C4 | semidirect |
| 60. #6386 | C2×C4 | semidirect |
| 293. C7 | #12940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741268 | 2 |
| C2×C7×#357 | 2 |
| C2×#89358 | 2 |
| #11728379 | 2 |
| #11728350 | 2 |
| #11725613 | 2 |
| #11725611 | 2 |
| #12940 | 7 |