Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
5502 conjugacy classes of subgroups; only the 3307 normal subgroups are shown.
This group has 5502 conjugacy classes of subgroups — too many to draw. Only its 3307 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. C2×#89707 | C2 | direct (N × H) |
| 6. C22×C42×C7 | C4 | semidirect |
| 10. #89707 | C22 | direct (N × H) |
| 19. C2×C42×C7 | C2×C4 | semidirect |
| 30. C22×C4×C7 | C4⋊C4 | semidirect |
| 38. C42×C7 | C22×C4 | semidirect |
| 44. C22×C42 | Dic7 | semidirect |
| 54. C2×C4×C7 | C2×C4⋊C4 | semidirect |
| 69. C2×C42 | C2×Dic7 | semidirect |
| 71. C22×C7 | #384 | semidirect |
| 78. C4×C7 | C22×C4⋊C4 | semidirect |
| 87. C22×C4 | C4⋊Dic7 | semidirect |
| 93. C42 | C22×Dic7 | semidirect |
| 94. C2×C7 | C2×#384 | semidirect |
| 107. C2×C4 | C2×C4⋊Dic7 | semidirect |
| 111. C7 | C22×#384 | semidirect |
| 112. C22 | #89707 | direct (N × H) |
| 120. C4 | C22×C4⋊Dic7 | semidirect |
| 121. C2 | C2×#89707 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C42×C7 | 2 |
| C23×C4⋊Dic7 | 2 |
| C2×#89707 | 2 |
| C22×#384 | 7 |