Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
532 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 99 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×#89915 | C2 | semidirect |
| 3. C2×#89681 | C2 | semidirect |
| 4. C2×C7×#350 | C2 | semidirect |
| 5. C2×#89305 | C2 | semidirect |
| 6. C2×#89298 | C2 | semidirect |
| 7. #11725623 | C2 | semidirect |
| 60. C2×Dic28 | D4 | semidirect |
| 68. C7×M32 | D4 | semidirect |
| 76. #6393 | D4 | semidirect |
| 87. C2×#350 | D7 | semidirect |
| 254. M32 | C22⋊D7 | semidirect |
| 396. C7 | #13308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89915 | 2 |
| #11741246 | 2 |
| C2×#89681 | 2 |
| C2×C7×#350 | 2 |
| C2×#89305 | 2 |
| C2×#89298 | 2 |
| #11725623 | 2 |
| #13308 | 7 |