Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
340 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 4. #11725349 | C2 | direct (N × H) |
| 6. C2×#6433 | C4 | semidirect |
| 13. #89828 | C4 | semidirect |
| 15. C2×C4×C7⋊C8 | C4 | semidirect |
| 37. #6433 | C2×C4 | semidirect |
| 47. C4×C7⋊C8 | C2×C4 | semidirect |
| 215. C2×C7 | #1414 | semidirect |
| 246. C7 | C2×#1414 | semidirect |
| 269. C2 | #11725349 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89828 | 2 |
| C2×C7×#354 | 2 |
| C2×#89337 | 2 |
| #11725349 | 2 |
| C2×#1414 | 7 |