Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
262 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 121 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. C7×#1371 | C2 | semidirect |
| 4. #11725306 | C2 | semidirect |
| 5. #11725275 | C2 | semidirect |
| 34. D7×C16 | C8 | semidirect |
| 39. #1371 | D7 | direct (N × H) |
| 58. C7×C16 | C2×C8 | semidirect |
| 60. C7⋊C16 | C2×C8 | semidirect |
| 140. C16 | C8×D7 | semidirect |
| 144. D7 | #1371 | direct (N × H) |
| 164. C7 | C2×#1371 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D7×C16 | 2 |
| D7×#335 | 2 |
| C7×#1371 | 2 |
| #11725306 | 2 |
| #11725275 | 2 |
| C2×#1371 | 7 |