Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
122 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 51 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. #10625058 | C2 | semidirect |
| 4. C23×#106 | C2 | semidirect |
| 5. C8×Dic23 | C2 | semidirect |
| 6. #10624992 | C2 | semidirect |
| 19. #67263 | C4 | semidirect |
| 31. Dic46 | C2×C4 | semidirect |
| 32. C8×C23 | C2×C4 | semidirect |
| 44. Dic23 | SD16 | semidirect |
| 53. #106 | D23 | semidirect |
| 57. C23 | C4×SD16 | semidirect |
| 83. C8 | C4×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67263 | 2 |
| #10625064 | 2 |
| #10625058 | 2 |
| C23×#106 | 2 |
| C8×Dic23 | 2 |
| #10624992 | 2 |
| #10624991 | 2 |
| C4×SD16 | 23 |