Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
402 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 402 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×#89452 | C2 | semidirect |
| 4. #11725536 | C2 | semidirect |
| 5. #11725464 | C2 | semidirect |
| 22. C2×C7×Q16 | Q8 | semidirect |
| 24. C2×C7×D8 | Q8 | semidirect |
| 121. C2×Q16 | Dic14 | semidirect |
| 123. C2×D8 | Dic14 | semidirect |
| 218. C7 | #13371 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89452 | 2 |
| C7×#1974 | 2 |
| C2×#89361 | 2 |
| #11725536 | 2 |
| #11725464 | 2 |
| #13371 | 7 |