Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
322 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
| 3. C2×C4⋊C4×C23 | C2 | semidirect |
| 6. C2×Dic23⋊C4 | C2 | semidirect |
| 7. C2×Dic23⋊C4 | C2 | semidirect |
| 8. #10625067 | C2 | direct (N × H) |
| 19. C2×Dic46 | C22 | semidirect |
| 20. C4⋊C4×C23 | C22 | semidirect |
| 23. Dic23⋊C4 | C22 | semidirect |
| 24. Dic23⋊C4 | C22 | semidirect |
| 28. C22×D23 | Q8 | semidirect |
| 51. C2×D23 | C2×Q8 | semidirect |
| 59. C2×C23 | C22⋊Q8 | semidirect |
| 69. C2×C4⋊C4 | D23 | semidirect |
| 72. C23 | C2×C22⋊Q8 | semidirect |
| 86. C4⋊C4 | C2×D23 | semidirect |
| 123. C2 | #10625067 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D23 | 2 |
| C22×Dic46 | 2 |
| C2×C4⋊C4×C23 | 2 |
| C2×(C2×D23)⋊C4 | 2 |
| C2×Dic23⋊C4 | 2 |
| #10625067 | 2 |
| C2×C22⋊Q8 | 23 |