Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
7118 conjugacy classes of subgroups; only the 1459 normal subgroups are shown.
This group has 7118 conjugacy classes of subgroups — too many to draw. Only its 1459 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 |
|---|---|---|
| 1. C24×C7×Q8 | C2 | semidirect |
| 3. C2×#90003 | C2 | direct (N × H) |
| 4. C22×C7⋊#95 | C2 | semidirect |
| 7. C23×C7×Q8 | C22 | semidirect |
| 12. #90003 | C22 | direct (N × H) |
| 13. C2×C7⋊#95 | C22 | semidirect |
| 18. C24×D7 | Q8 | semidirect |
| 22. C22×C7×Q8 | C23 | semidirect |
| 31. C7⋊#95 | C23 | semidirect |
| 32. C24×Q8 | D7 | semidirect |
| 45. C23×D7 | C2×Q8 | semidirect |
| 60. C23×Q8 | C2×D7 | semidirect |
| 80. C22×D7 | C22×Q8 | semidirect |
| 95. C22×Q8 | C22×D7 | semidirect |
| 105. C22×C7 | #393 | semidirect |
| 140. C2×C7 | C2×#393 | semidirect |
| 166. C7 | C22×#393 | semidirect |
| 171. C22 | #90003 | direct (N × H) |
| 181. C2 | C2×#90003 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C7×Q8 | 2 |
| C23×(C2×D7)⋊C4 | 2 |
| C2×#90003 | 2 |
| C22×C7⋊#95 | 2 |
| C22×#393 | 7 |