Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
3798 conjugacy classes of subgroups; only the 923 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 923 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. C2×C7×#383 | C2 | semidirect |
| 3. C2×#89709 | C2 | semidirect |
| 4. #11731743 | C2 | direct (N × H) |
| 5. C2×#89437 | C2 | semidirect |
| 10. C2×#6437 | C4 | semidirect |
| 12. C7×#383 | C22 | semidirect |
| 15. #89709 | C22 | semidirect |
| 16. #89437 | C22 | semidirect |
| 24. C22×D28 | C2×C4 | semidirect |
| 28. C2×C42×C7 | C2×C4 | semidirect |
| 32. #6437 | C2×C4 | semidirect |
| 39. C2×#383 | D7 | semidirect |
| 55. C2×D28 | C22×C4 | semidirect |
| 58. C42×C7 | C22×C4 | semidirect |
| 68. #383 | C2×D7 | semidirect |
| 102. C2×C42 | C4×D7 | semidirect |
| 136. C42 | C2×C4×D7 | semidirect |
| 137. C2×C7 | #2380 | semidirect |
| 159. C7 | C2×#2380 | semidirect |
| 172. C2 | #11731743 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6437 | 2 |
| C2×C7×#383 | 2 |
| C2×#89709 | 2 |
| #11731743 | 2 |
| C2×#89437 | 2 |
| C2×#2380 | 7 |