Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
232 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 232 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 |
|---|---|---|
| 2. C16×Dic14 | C2 | semidirect |
| 4. C7×#1312 | C2 | semidirect |
| 5. #11725312 | C2 | semidirect |
| 7. #11725246 | C2 | semidirect |
| 51. #1312 | D7 | semidirect |
| 68. #1132 | C16 | semidirect |
| 103. Dic14 | C2×C16 | semidirect |
| 107. C7×C8 | C2×C16 | semidirect |
| 191. C8 | D7×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 |
|---|---|
| C16×D28 | 2 |
| C16×Dic14 | 2 |
| C8×#1132 | 2 |
| C7×#1312 | 2 |
| #11725312 | 2 |
| #11725309 | 2 |
| #11725246 | 2 |
| SD16⋊C16 | 7 |