Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 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. C16×Dic14 | C2 | semidirect |
| 5. #11725364 | C2 | semidirect |
| 6. #11725360 | C2 | semidirect |
| 7. #11725304 | C2 | semidirect |
| 73. C7×C16 | SD16 | semidirect |
| 103. Dic14 | M32 | semidirect |
| 168. C16 | #1142 | semidirect |
| 194. C7 | #12050 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2169 | 2 |
| C8×#1142 | 2 |
| C16×Dic14 | 2 |
| D4⋊(C7⋊C16) | 2 |
| #11725364 | 2 |
| #11725360 | 2 |
| #11725304 | 2 |
| #12050 | 7 |