Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
232 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #11727034 | C2 | semidirect |
| 5. #11725361 | C2 | semidirect |
| 6. #11725312 | C2 | semidirect |
| 7. #11725305 | C2 | semidirect |
| 63. #1142 | C16 | semidirect |
| 103. Dic14 | C2×C16 | semidirect |
| 111. C7⋊C8 | C2×C16 | semidirect |
| 194. C7 | SD16⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×C7⋊C16 | 2 |
| C8×#1142 | 2 |
| #11727034 | 2 |
| C7×D4⋊C16 | 2 |
| #11725361 | 2 |
| #11725312 | 2 |
| #11725305 | 2 |
| SD16⋊C16 | 7 |