Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
364 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 95 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. #11735924 | C2 | semidirect |
| 4. #11725541 | C2 | semidirect |
| 5. #11725469 | C2 | semidirect |
| 21. C2×C7×Q16 | Q8 | semidirect |
| 23. C2×C7×D8 | Q8 | semidirect |
| 120. C2×Q16 | Dic14 | semidirect |
| 122. C2×D8 | Dic14 | semidirect |
| 218. C7 | #13373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11735924 | 2 |
| C7×#1975 | 2 |
| #11729830 | 2 |
| #11725541 | 2 |
| #11725469 | 2 |
| #13373 | 7 |