Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 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. C22×Dic46 | C2 | semidirect |
| 5. C2×C4⋊Dic23 | C2 | semidirect |
| 6. C2×Dic23⋊C4 | C2 | semidirect |
| 7. C2×Dic23⋊C4 | C2 | semidirect |
| 8. #10625049 | C2 | direct (N × H) |
| 19. C2×Dic46 | C22 | semidirect |
| 22. C4⋊Dic23 | C22 | semidirect |
| 23. Dic23⋊C4 | C22 | semidirect |
| 24. Dic23⋊C4 | C22 | semidirect |
| 27. C23×C23 | Q8 | semidirect |
| 49. C22×C23 | C2×Q8 | semidirect |
| 60. C2×C23 | C22⋊Q8 | semidirect |
| 72. C23 | C2×C22⋊Q8 | semidirect |
| 91. C23 | Dic46 | semidirect |
| 112. C22 | C2×Dic46 | semidirect |
| 123. C2 | #10625049 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic23 | 2 |
| C22×Dic46 | 2 |
| C2×C22⋊C4×C23 | 2 |
| C2×C22⋊Dic23 | 2 |
| C2×C4⋊Dic23 | 2 |
| C2×Dic23⋊C4 | 2 |
| #10625049 | 2 |
| C2×C22⋊Q8 | 23 |